Rings and Categories of Modules (Graduate Texts in Mathematics)

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9780387978451: Rings and Categories of Modules (Graduate Texts in Mathematics)

This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil­ iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de­ composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon.

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About the Author:

Born in Brandon, Manitoba, in 1919, Frank W. Anderson was orphaned at 18 months and grew up in foster homes, reform schools and jails. At age 16, he was convicted of killing a prison guard and was sentenced to death. This was commuted to life and he spent the next 15 years in a penitentiary. There he completed his high school education and became the first prisoner in Canada to take university courses behind bars. Paroled in 1951, he completed a BA and an MA in social work from the University of Toronto. He then joined the John Howard Society and became a parole officer. He developed a two-year course in human behaviour that was adopted by several colleges, and he was appointed to the National Parole Board in 1974, placed in charge of the region covering Manitoba, Saskatchewan, Alberta and the Northwest Territories. He held this position until he retired. In 1998, the University of Ottawa created the Frank W. Anderson Archives of Criminology to serve as a resource centre for students across Canada. He married Edna Marshal in 1955 and they had two children. He moved to Saskatoon after retiring and managed Frontier Books, publishing more than 100 books on Canadian history written by himself and other authors, including Ken Liddell and W.O. Mitchell. He also wrote a book about women who were executed in Canada, "A Dance with Death: Canadian Women on the Gallows". Although he was later based in Calgary, Frank wrote, edited and produced numerous titles pertaining to British Columbia.

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