Ring theory exercises at the graduate level

Do you know any book or an online source that contains exercises on ring theory? I've solved some exercises of Lang's Algebra and Dummit & Foote's Abstract Algebra but there is a huge gap between these two. I need a graduate level problem book but not as hard as Lang. Thanks in advance.

How about Exercises in Classical Ring Theory and Exercises in Basic Ring Theory?

Harry C. Hutchins, Examples of Commutative Rings has many interesting examples (and/or counterexamples) which may serve as good exercises, with hints and literature references. The book was based upon Hutchins' 1978 Chicago thesis (under Kaplansky). It was apparently intended as a companion to Kap's classic textbook Commutative Rings (many references refer to Kap's book). There is also a 3 page list of errata, updates,... dated July 1983, which is distributed with the book. Below is the AMS Math Review.

Hutchins, Harry C. 83a:13001 13-02
Examples of commutative rings.
Polygonal Publ. House, Washington, N. J., 1981. vii+167 pp. ISBN 0-936428-05-8

The book is divided into two parts: a brief sketch of commutative ring theory which includes pertinent definitions along with main results without proof (but with ample references), and Part II, the 180 examples. The examples do cover a very large range of topics. Although most of them appear elsewhere, they are enhanced by a fairly complete listing of their properties. Example 67, for instance, is M. Hochster's counterexample to the polynomial cancellation problem, and it lists a number of properties of the two rings that were not given in the original paper Proc. Amer. Math. Soc. 34 (1972), no. 1, 81 - 82; MR 45 #3394. Some of the examples appear more than once, since many rings exhibit more than one interesting property. ($\rm\:R = K[x, y, z]\:$ is used in Examples 6 and 22.) The examples are grouped into areas, but a drawback is that these have not been labeled and separated off. In addition, the Index is for Part I and definitions only, and this means that searching for a specific example with certain properties can be time consuming.

The book can be used as a supplement to one of the standard texts in commutative ring theory, and it does appear to complement the monograph by I. Kaplansky Commutative rings, Allyn and Bacon, Boston, Mass., 1970; MR 40 #7234; second edition, Univ. Chicago Press, Chicago, Ill., 1974; MR 49 #10674.

Reviewed by Jon L. Johnson

In the UK most (leading) unis provide problem sets openly.