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I am studying ring theory in this semester. I am new to this theory. Hence, I would like to have some recommendations on what books should be used for ring theory(beginner). If possible, I would like to have a book on theory and a lot of problems( include solution would be nicer,if possible). Can anyone give some recommendations?

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Personally, I am fond of the following two books in the area you noted:

  • A First Course in Rings and Ideals by D.M. Burton.

  • Contemporary Abstract Algebra by J.A.Gallian.

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Yu.Drozd, V.Kirichenko, Finite Dimensional Algebras (for 1st reading)

J.Lambek, Lectures on Rings and Modules (for 2nd reading)

I.Herstein, Noncommutative Rings (most preferable for me, but without exercises)

M.Atiyah, I.McDonald, Introduction to Commutative Algebra (if you will study algebraic geometry in the future)

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  • $\begingroup$ but aren't these test meant for graduate students? $\endgroup$ – Idonknow Mar 24 '13 at 13:16
  • $\begingroup$ It depends on your level. I think first 2 books are OK. If they are difficult for you, start with some books on general algebra. There are many of them (for example, N.Jacobson, Basic Algebra, v.I; P.Grillet, Abstract Algebra, etc.) $\endgroup$ – Boris Novikov Mar 24 '13 at 13:49

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