Quasi-Frobenius Rings (Cambridge Tracts in Mathematics)
Publisher: Cambridge University Press
Published: September 8, 2003
Language: eng
Format: Hardcover
Number of pages: 326
ISBN-13: 9780521815932
Subjects: Algebraic number theory; Fields & rings; Science/Mathematics; Rings; Mathematics; Algebra - General; Mathematics / Algebra / General; Group Theory; Quasi-Frobenius rings
First sentence: To make this monograph as self-contained as possible, this preliminary chapter contains basic characterizations of quasi-Frobenius and pseudo-Frobenius rings, together with the necessary background material.
Description: A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all four combinations are equivalent). The study of these rings grew out of the theory of representations of a finite group as a group of matrices over a field, and the subject is intimately related to duality, the duality from right to left modules induced by the hom functor and the duality related to annihilators. The present extent of the theory is vast, and this book makes no attempt to be encyclopedic; instead it provides an elementary, self-contained account of the basic facts about these rings at a level allowing researchers and graduate students to gain entry to the field.