Librería Bonilla. Desde 1950

	Título: Lectures On Rings And Modules
	Autor: Joachim Lambek	Precio: Desconocido
	Editorial: American Mathematical Society	Año: 1986
	Tema:	Edición: 2ª
	Sinopsis	ISBN: 9780821849002
	Due to their clarity and intelligible presentation, these lectures on rings and modules are a particularly successful introduction to the surrounding circle of ideas. --Zentralblatt MATH This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments. Reviews "An introduction to associative rings and modules which requires of the reader only the mathematical maturity which one would attain in a first-year graduate algebra [course] ... in order to make the contents of the book as accessible as possible, the author develops all the fundamentals he will need. In addition to covering the basic topics ... the author covers some topics not so readily available to the nonspecialist ... the chapters are written to be as independent as possible ... [which will be appreciated by] students making their first acquaintance with the subject ... one of the most successful features of the book is that it can be read by graduate students with little or no help from a specialist." -- American Mathematical Monthly "An excellent textbook and "classical" reference-text in associative ring theory." -- Zentralblatt MATH Table of Contents Fundamental Concepts of Algebra 1.1 Rings and related algebraic systems 1.2 Subrings, homomorphisms, ideals 1.3 Modules, direct products, and direct sums 1.4 Classical isomorphism theorems Selected Topics on Commutative Rings 2.1 Prime ideals in commutative rings 2.2 Prime ideals in special commutative rings 2.3 The complete ring of quotients of a commutative ring 2.4 Rings of quotients of commutative semiprime rings 2.5 Prime ideal spaces Classical Theory of Associative Rings 3.1 Primitive rings 3.2 Radicals 3.3 Completely reducible modules 3.4 Completely reducible rings 3.5 Artinian and Noetherian rings 3.6 On lifting idempotents 3.7 Local and semiperfect rings Injectivity and Related Concepts 4.1 Projective modules 4.2 Injective modules 4.3 The complete ring of quotients 4.4 Rings of endomorphisms of injective modules 4.5 Regular rings of quotients 4.6 Classical rings of quotients 4.7 The Faith-Utumi theorem Introduction to Homological Algebra 5.1 Tensor products of modules 5.2 Hom and ? as functors 5.3 Exact sequences 5.4 Flat modules 5.5 Torsion and extension products Appendixes Comments Bibliography Index

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