Next semester I will take a course about Ring and Module Theory. Can anyone tell me the best texbooks and problems books about it. I only know some famous problems books such as Exercises in Classical Ring Theory, Exercises in Modules and Rings, Exercises in Basic Ring Theory.
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There are two Lams books Lectures in modules and rings and A first course in noncommutative rings those two books cover pretty much everything you may wanna know about modules. As you mentioned there is Lams, Exercise in modules and rings. – user52045 Nov 25 '13 at 15:36
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possible duplicate of Some basic book to start with modules? or http://math.stackexchange.com/questions/339500/ .. or ... just use the search function guys! – Martin Brandenburg Nov 25 '13 at 15:38
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Joseph Rotman - An Introduction to Homological Algebra (2nd edition)
is a great book about homological algebra, but it contains many sections about modules and rings. I advise you to give it a look since it is a wonderfully written book!
Abramo
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I'll agree that's a great book, but not for the basics on Ring and Module theory unless one is solely concerned with the homological aspects of ring theory. – J. Gaddis Nov 25 '13 at 15:34
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Louis Halle Rowen - Ring Theory
This is a great introduction to commutative and noncommutative ring theory as well as modules over rings. It also includes an overview of some key homological results which are covered (in greater depth for commutative rings) in the book Abramo mentioned.
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I highly recommend Matsumura's book on Commutative Ring Theory which deals with rings and modules. This is a good book in preparation of a course in algebraic geometry.
BIS HD
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