Non-Commutative Algebra book
5
$begingroup$
I am currently having a Master in topics such as Algebra, Geometry and Number Theory and recently I started studying Representation Theory where I've seen definition, theorems and propositions concerning rings that are non-commutative in general. I am wondering if there's any "standard" book(s) that can introduce me to the theory of non-commutative algebra.
book-recommendation noncommutative-algebra
edited Apr 3 at 16:08
J. W. Tanner
5,0531520
asked Apr 3 at 15:51
CorneliusCornelius
32017
$endgroup$
add a comment |
5
$begingroup$
I am currently having a Master in topics such as Algebra, Geometry and Number Theory and recently I started studying Representation Theory where I've seen definition, theorems and propositions concerning rings that are non-commutative in general. I am wondering if there's any "standard" book(s) that can introduce me to the theory of non-commutative algebra.
book-recommendation noncommutative-algebra
edited Apr 3 at 16:08
J. W. Tanner
5,0531520
asked Apr 3 at 15:51
CorneliusCornelius
32017
$endgroup$
$begingroup$
Lam's "A First Course in Noncommutative Rings" and "Lectures on Modules and Rings" are both gems. (The former is the more introductory of the two, as the name suggests.)
$endgroup$
– Alex Wertheim
Apr 3 at 15:57
$begingroup$
I think I will go with "A First Course in Noncommutative Rings" by Lam. Thank you Alex for your answer and I look forward for more book recommendations.
$endgroup$
– Cornelius
Apr 3 at 16:12
add a comment |
5
5
5
1
$begingroup$
I am currently having a Master in topics such as Algebra, Geometry and Number Theory and recently I started studying Representation Theory where I've seen definition, theorems and propositions concerning rings that are non-commutative in general. I am wondering if there's any "standard" book(s) that can introduce me to the theory of non-commutative algebra.
book-recommendation noncommutative-algebra
edited Apr 3 at 16:08
J. W. Tanner
5,0531520
asked Apr 3 at 15:51
CorneliusCornelius
32017
$endgroup$
I am currently having a Master in topics such as Algebra, Geometry and Number Theory and recently I started studying Representation Theory where I've seen definition, theorems and propositions concerning rings that are non-commutative in general. I am wondering if there's any "standard" book(s) that can introduce me to the theory of non-commutative algebra.
book-recommendation noncommutative-algebra
book-recommendation noncommutative-algebra
edited Apr 3 at 16:08
J. W. Tanner
5,0531520
asked Apr 3 at 15:51
CorneliusCornelius
32017
edited Apr 3 at 16:08
J. W. Tanner
5,0531520
asked Apr 3 at 15:51
CorneliusCornelius
32017
edited Apr 3 at 16:08
J. W. Tanner
5,0531520
edited Apr 3 at 16:08
J. W. Tanner
5,0531520
edited Apr 3 at 16:08
J. W. Tanner
5,0531520
5,0531520
asked Apr 3 at 15:51
CorneliusCornelius
32017
asked Apr 3 at 15:51
CorneliusCornelius
32017
asked Apr 3 at 15:51
CorneliusCornelius
32017
32017
$begingroup$
Lam's "A First Course in Noncommutative Rings" and "Lectures on Modules and Rings" are both gems. (The former is the more introductory of the two, as the name suggests.)
$endgroup$
– Alex Wertheim
Apr 3 at 15:57
$begingroup$
I think I will go with "A First Course in Noncommutative Rings" by Lam. Thank you Alex for your answer and I look forward for more book recommendations.
$endgroup$
– Cornelius
Apr 3 at 16:12
add a comment |
$begingroup$
Lam's "A First Course in Noncommutative Rings" and "Lectures on Modules and Rings" are both gems. (The former is the more introductory of the two, as the name suggests.)
$endgroup$
– Alex Wertheim
Apr 3 at 15:57
$begingroup$
I think I will go with "A First Course in Noncommutative Rings" by Lam. Thank you Alex for your answer and I look forward for more book recommendations.
$endgroup$
– Cornelius
Apr 3 at 16:12
$begingroup$
Lam's "A First Course in Noncommutative Rings" and "Lectures on Modules and Rings" are both gems. (The former is the more introductory of the two, as the name suggests.)
$endgroup$
– Alex Wertheim
Apr 3 at 15:57
$begingroup$
Lam's "A First Course in Noncommutative Rings" and "Lectures on Modules and Rings" are both gems. (The former is the more introductory of the two, as the name suggests.)
$endgroup$
– Alex Wertheim
Apr 3 at 15:57
$begingroup$
I think I will go with "A First Course in Noncommutative Rings" by Lam. Thank you Alex for your answer and I look forward for more book recommendations.
$endgroup$
– Cornelius
Apr 3 at 16:12
$begingroup$
I think I will go with "A First Course in Noncommutative Rings" by Lam. Thank you Alex for your answer and I look forward for more book recommendations.
$endgroup$
– Cornelius
Apr 3 at 16:12
add a comment |
1 Answer
1
active
oldest
votes
4
$begingroup$
Ones I have used extensively
First Course in Noncommutative Rings by T.Y. Lam- Isaacs Graduate algebra
Basic abstract algebra by P. B. Bhattacharya, S. K. Jain & Nagpaul
Others often mentioned as standard (but I did not really use)
- McCoy's The theory of rings
- Dummit and Foote's Abstract algebra
- Hungerford's Algebra
Noncommutative rings by Herstein
Ones I have not used extensively but would recommend
- Lambek's Lectures on rings and modules
- Jacobson's Basic Algebra volumes I and II
Books that are a step up from an introduction
- Anderson and Fuller's Rings and categories of modules
- Lam's Lectures on modules and rings
- Louis Rowen's books and Carl Faith's books on algebra and ring theory.
answered Apr 3 at 16:43
rschwiebrschwieb
108k12105253
$endgroup$
$begingroup$
A good method might just be to search for "Artin-Wedderburn theorem" in google books and just pick anything promising from the tons of hits that come back. That is a standard introductory topic in noncommutative algebra.
$endgroup$
– rschwieb
Apr 3 at 16:47
$begingroup$
Wow, thats a nice collection to have. I will get as many of them as possible and look around while studying. Thanks rschwieb!
$endgroup$
– Cornelius
Apr 3 at 16:55
$begingroup$
Studying Artin-Wedderburn theorem for representation theory was exactly the spark tha led me to search for more into Non-Commutative Algebra
$endgroup$
– Cornelius
Apr 3 at 16:57
$begingroup$
If I can make an addition, I'd say that Farb and Dennis' Noncommutative Algebra is pretty good as well. It's treatment of semisimplicity and the Jacobson radical are quite nice, and its approach to central simple division algebras is all based on going to the Brauer Group and seeing $H^2$ from a different light than the usual Galois cohomological perspective. They also focus on homological techniques, which are nice to see and useful if you're into $p$-adic representation theory.
$endgroup$
– Geoff
Apr 3 at 18:18
$begingroup$
Thanks Geoff, also added on my list. It is always nice to have many books on the same topic in order to see many different perspectives.
$endgroup$
– Cornelius
Apr 4 at 12:33
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
4
$begingroup$
Ones I have used extensively
First Course in Noncommutative Rings by T.Y. Lam- Isaacs Graduate algebra
Basic abstract algebra by P. B. Bhattacharya, S. K. Jain & Nagpaul
Others often mentioned as standard (but I did not really use)
- McCoy's The theory of rings
- Dummit and Foote's Abstract algebra
- Hungerford's Algebra
Noncommutative rings by Herstein
Ones I have not used extensively but would recommend
- Lambek's Lectures on rings and modules
- Jacobson's Basic Algebra volumes I and II
Books that are a step up from an introduction
- Anderson and Fuller's Rings and categories of modules
- Lam's Lectures on modules and rings
- Louis Rowen's books and Carl Faith's books on algebra and ring theory.
answered Apr 3 at 16:43
rschwiebrschwieb
108k12105253
$endgroup$
$begingroup$
A good method might just be to search for "Artin-Wedderburn theorem" in google books and just pick anything promising from the tons of hits that come back. That is a standard introductory topic in noncommutative algebra.
$endgroup$
– rschwieb
Apr 3 at 16:47
$begingroup$
Wow, thats a nice collection to have. I will get as many of them as possible and look around while studying. Thanks rschwieb!
$endgroup$
– Cornelius
Apr 3 at 16:55
$begingroup$
Studying Artin-Wedderburn theorem for representation theory was exactly the spark tha led me to search for more into Non-Commutative Algebra
$endgroup$
– Cornelius
Apr 3 at 16:57
$begingroup$
If I can make an addition, I'd say that Farb and Dennis' Noncommutative Algebra is pretty good as well. It's treatment of semisimplicity and the Jacobson radical are quite nice, and its approach to central simple division algebras is all based on going to the Brauer Group and seeing $H^2$ from a different light than the usual Galois cohomological perspective. They also focus on homological techniques, which are nice to see and useful if you're into $p$-adic representation theory.
$endgroup$
– Geoff
Apr 3 at 18:18
$begingroup$
Thanks Geoff, also added on my list. It is always nice to have many books on the same topic in order to see many different perspectives.
$endgroup$
– Cornelius
Apr 4 at 12:33
add a comment |
4
$begingroup$
Ones I have used extensively
First Course in Noncommutative Rings by T.Y. Lam- Isaacs Graduate algebra
Basic abstract algebra by P. B. Bhattacharya, S. K. Jain & Nagpaul
Others often mentioned as standard (but I did not really use)
- McCoy's The theory of rings
- Dummit and Foote's Abstract algebra
- Hungerford's Algebra
Noncommutative rings by Herstein
Ones I have not used extensively but would recommend
- Lambek's Lectures on rings and modules
- Jacobson's Basic Algebra volumes I and II
Books that are a step up from an introduction
- Anderson and Fuller's Rings and categories of modules
- Lam's Lectures on modules and rings
- Louis Rowen's books and Carl Faith's books on algebra and ring theory.
answered Apr 3 at 16:43
rschwiebrschwieb
108k12105253
$endgroup$
$begingroup$
A good method might just be to search for "Artin-Wedderburn theorem" in google books and just pick anything promising from the tons of hits that come back. That is a standard introductory topic in noncommutative algebra.
$endgroup$
– rschwieb
Apr 3 at 16:47
$begingroup$
Wow, thats a nice collection to have. I will get as many of them as possible and look around while studying. Thanks rschwieb!
$endgroup$
– Cornelius
Apr 3 at 16:55
$begingroup$
Studying Artin-Wedderburn theorem for representation theory was exactly the spark tha led me to search for more into Non-Commutative Algebra
$endgroup$
– Cornelius
Apr 3 at 16:57
$begingroup$
If I can make an addition, I'd say that Farb and Dennis' Noncommutative Algebra is pretty good as well. It's treatment of semisimplicity and the Jacobson radical are quite nice, and its approach to central simple division algebras is all based on going to the Brauer Group and seeing $H^2$ from a different light than the usual Galois cohomological perspective. They also focus on homological techniques, which are nice to see and useful if you're into $p$-adic representation theory.
$endgroup$
– Geoff
Apr 3 at 18:18
$begingroup$
Thanks Geoff, also added on my list. It is always nice to have many books on the same topic in order to see many different perspectives.
$endgroup$
– Cornelius
Apr 4 at 12:33
add a comment |
4
4
4
$begingroup$
Ones I have used extensively
First Course in Noncommutative Rings by T.Y. Lam- Isaacs Graduate algebra
Basic abstract algebra by P. B. Bhattacharya, S. K. Jain & Nagpaul
Others often mentioned as standard (but I did not really use)
- McCoy's The theory of rings
- Dummit and Foote's Abstract algebra
- Hungerford's Algebra
Noncommutative rings by Herstein
Ones I have not used extensively but would recommend
- Lambek's Lectures on rings and modules
- Jacobson's Basic Algebra volumes I and II
Books that are a step up from an introduction
- Anderson and Fuller's Rings and categories of modules
- Lam's Lectures on modules and rings
- Louis Rowen's books and Carl Faith's books on algebra and ring theory.
answered Apr 3 at 16:43
rschwiebrschwieb
108k12105253
$endgroup$
Ones I have used extensively
First Course in Noncommutative Rings by T.Y. Lam- Isaacs Graduate algebra
Basic abstract algebra by P. B. Bhattacharya, S. K. Jain & Nagpaul
Others often mentioned as standard (but I did not really use)
- McCoy's The theory of rings
- Dummit and Foote's Abstract algebra
- Hungerford's Algebra
Noncommutative rings by Herstein
Ones I have not used extensively but would recommend
- Lambek's Lectures on rings and modules
- Jacobson's Basic Algebra volumes I and II
Books that are a step up from an introduction
- Anderson and Fuller's Rings and categories of modules
- Lam's Lectures on modules and rings
- Louis Rowen's books and Carl Faith's books on algebra and ring theory.
answered Apr 3 at 16:43
rschwiebrschwieb
108k12105253
edited Apr 3 at 16:49
answered Apr 3 at 16:43
rschwiebrschwieb
108k12105253
answered Apr 3 at 16:43
rschwiebrschwieb
108k12105253
answered Apr 3 at 16:43
rschwiebrschwieb
108k12105253
108k12105253
$begingroup$
A good method might just be to search for "Artin-Wedderburn theorem" in google books and just pick anything promising from the tons of hits that come back. That is a standard introductory topic in noncommutative algebra.
$endgroup$
– rschwieb
Apr 3 at 16:47
$begingroup$
Wow, thats a nice collection to have. I will get as many of them as possible and look around while studying. Thanks rschwieb!
$endgroup$
– Cornelius
Apr 3 at 16:55
$begingroup$
Studying Artin-Wedderburn theorem for representation theory was exactly the spark tha led me to search for more into Non-Commutative Algebra
$endgroup$
– Cornelius
Apr 3 at 16:57
$begingroup$
If I can make an addition, I'd say that Farb and Dennis' Noncommutative Algebra is pretty good as well. It's treatment of semisimplicity and the Jacobson radical are quite nice, and its approach to central simple division algebras is all based on going to the Brauer Group and seeing $H^2$ from a different light than the usual Galois cohomological perspective. They also focus on homological techniques, which are nice to see and useful if you're into $p$-adic representation theory.
$endgroup$
– Geoff
Apr 3 at 18:18
$begingroup$
Thanks Geoff, also added on my list. It is always nice to have many books on the same topic in order to see many different perspectives.
$endgroup$
– Cornelius
Apr 4 at 12:33
add a comment |
$begingroup$
A good method might just be to search for "Artin-Wedderburn theorem" in google books and just pick anything promising from the tons of hits that come back. That is a standard introductory topic in noncommutative algebra.
$endgroup$
– rschwieb
Apr 3 at 16:47
$begingroup$
Wow, thats a nice collection to have. I will get as many of them as possible and look around while studying. Thanks rschwieb!
$endgroup$
– Cornelius
Apr 3 at 16:55
$begingroup$
Studying Artin-Wedderburn theorem for representation theory was exactly the spark tha led me to search for more into Non-Commutative Algebra
$endgroup$
– Cornelius
Apr 3 at 16:57
$begingroup$
If I can make an addition, I'd say that Farb and Dennis' Noncommutative Algebra is pretty good as well. It's treatment of semisimplicity and the Jacobson radical are quite nice, and its approach to central simple division algebras is all based on going to the Brauer Group and seeing $H^2$ from a different light than the usual Galois cohomological perspective. They also focus on homological techniques, which are nice to see and useful if you're into $p$-adic representation theory.
$endgroup$
– Geoff
Apr 3 at 18:18
$begingroup$
Thanks Geoff, also added on my list. It is always nice to have many books on the same topic in order to see many different perspectives.
$endgroup$
– Cornelius
Apr 4 at 12:33
$begingroup$
A good method might just be to search for "Artin-Wedderburn theorem" in google books and just pick anything promising from the tons of hits that come back. That is a standard introductory topic in noncommutative algebra.
$endgroup$
– rschwieb
Apr 3 at 16:47
$begingroup$
A good method might just be to search for "Artin-Wedderburn theorem" in google books and just pick anything promising from the tons of hits that come back. That is a standard introductory topic in noncommutative algebra.
$endgroup$
– rschwieb
Apr 3 at 16:47
$begingroup$
Wow, thats a nice collection to have. I will get as many of them as possible and look around while studying. Thanks rschwieb!
$endgroup$
– Cornelius
Apr 3 at 16:55
$begingroup$
Wow, thats a nice collection to have. I will get as many of them as possible and look around while studying. Thanks rschwieb!
$endgroup$
– Cornelius
Apr 3 at 16:55
$begingroup$
Studying Artin-Wedderburn theorem for representation theory was exactly the spark tha led me to search for more into Non-Commutative Algebra
$endgroup$
– Cornelius
Apr 3 at 16:57
$begingroup$
Studying Artin-Wedderburn theorem for representation theory was exactly the spark tha led me to search for more into Non-Commutative Algebra
$endgroup$
– Cornelius
Apr 3 at 16:57
$begingroup$
If I can make an addition, I'd say that Farb and Dennis' Noncommutative Algebra is pretty good as well. It's treatment of semisimplicity and the Jacobson radical are quite nice, and its approach to central simple division algebras is all based on going to the Brauer Group and seeing $H^2$ from a different light than the usual Galois cohomological perspective. They also focus on homological techniques, which are nice to see and useful if you're into $p$-adic representation theory.
$endgroup$
– Geoff
Apr 3 at 18:18
$begingroup$
If I can make an addition, I'd say that Farb and Dennis' Noncommutative Algebra is pretty good as well. It's treatment of semisimplicity and the Jacobson radical are quite nice, and its approach to central simple division algebras is all based on going to the Brauer Group and seeing $H^2$ from a different light than the usual Galois cohomological perspective. They also focus on homological techniques, which are nice to see and useful if you're into $p$-adic representation theory.
$endgroup$
– Geoff
Apr 3 at 18:18
$begingroup$
Thanks Geoff, also added on my list. It is always nice to have many books on the same topic in order to see many different perspectives.
$endgroup$
– Cornelius
Apr 4 at 12:33
$begingroup$
Thanks Geoff, also added on my list. It is always nice to have many books on the same topic in order to see many different perspectives.
$endgroup$
– Cornelius
Apr 4 at 12:33
add a comment |
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$begingroup$
Lam's "A First Course in Noncommutative Rings" and "Lectures on Modules and Rings" are both gems. (The former is the more introductory of the two, as the name suggests.)
$endgroup$
– Alex Wertheim
Apr 3 at 15:57
$begingroup$
I think I will go with "A First Course in Noncommutative Rings" by Lam. Thank you Alex for your answer and I look forward for more book recommendations.
$endgroup$
– Cornelius
Apr 3 at 16:12