Non-Commutative Algebra book 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.

Ones I have used extensively


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*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)


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*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


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*Lambek's Lectures on rings and modules

*Jacobson's Basic Algebra volumes I and II


Books that are a step up from an introduction


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*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.

