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Foundations of module and ring theory. A handbook for study and research. Revised and updated Engl. ed. (English) Zbl 0746.16001
Algebra, Logic and Applications. 3. Philadelphia etc.: Gordon and Breach Science Publishers. xi, 606 p. (1991).
This book is a revised and updated English edition of the monograph by the same author, “Grundlagen der Modul- und Ringtheorie” (Verlag Reinhard Fischer, München 1988). This English edition contains besides several improvements and minor changes, a number of additional exercises and references, as well as some new results. So, in paragraph 48.16 a characterization of cogenerator modules with commutative endomorphism ring is given; two new paragraphs, namely 51.12 and 51.13, based on a recent joint paper of the reviewer and the author of the book show that a category \(\sigma[M]\) which has a generator with right perfect endomorphism ring also has a projective generator; in 52.7 and 52.8 the functor rings of regular and resp. semisimple modules are characterized; finally, three new paragraphs, 54.4, 54.5 and 54.6, based on a recent paper of the author on modules with the Kulikov property, were added. A description of the content of the German edition of the book, showing its main features, was given by G. Krause in Zbl 0657.16001; so, we restrict ourselves only to say that this English edition is very worthwhile and it is a welcome addition to the existent literature in Module and Ring Theory, that should be on the shelf of anyone active in these domains.

16-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras
16D90 Module categories in associative algebras
18E15 Grothendieck categories (MSC2010)