โ Scribed by Frank W. Anderson, Kent R. Fuller (auth.)
No coin nor oath required. For personal study only.
This book is intended to provide a self-contained account of much of the theory of rings and modules. The theme of the text throughout is the relationship between the one-sided ideal structure a ring may possess and the behavior of its categories of modules. Following a brief outline of the foundations, the book begins with the basic definitions and properties of rings, modules and homomorphisms. The remainder of the text gives comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, decomposition theory, and semiperfect and perfect rings. This second edition includes a chapter containing many of the classical results on Artinian rings that have helped form the foundation for much of contemporary research on the representation theory of Artinian rings and finite-dimensional algebras.
Physics, general
๐ SIMILAR VOLUMES
In this paper we describe how to give a particular global category of rings and modules the structure of a relaxed multicategory, and we describe an algebra in this relaxed multicategory such that vertex algebras appear as such algebras.