A first course in noncommutative rings. 2nd ed. (English) Zbl 0980.16001

Graduate Texts in Mathematics. 131. New York, NY: Springer. xix, 385 p. DM 106.89, sFr. 94.16, £37.00, $ 49.95/pbk; DM 181.79, sFr. 156.76, £62.50, $ 79.95/hbk (2001).
This is the second edition of the textbook with the same title (1991; Zbl 0728.16001). From the author’s preface to the second edition: In this new edition of “First Course”, the entire text has been retyped, some proofs were rewritten, and numerous improvements in the exposition have been included. The original chapters and sections have remained unchanged, with exception of an Appendix (on uniserial modules) to §20. The original exercises in the first edition have been replaced by the 400 exercises in the problem book [T. Y. Lam, Exercises in classical ring theory, Springer-Verlag (1995; Zbl 0823.16001)], and I have added at least 30 more in this edition for the convenience of the reader.


16-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16L30 Noncommutative local and semilocal rings, perfect rings
16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras)