Non-Commutative Algebra book

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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.

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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.