Description

Book Synopsis
Suitable for an undergraduate first course in ring theory, this work discusses the various aspects of commutative and noncommutative ring theory. It begins with basic module theory and then proceeds to surveying various special classes of rings (Wedderbum, Artinian and Noetherian rings, hereditary rings and Dedekind domains.).

Table of Contents
Projective modules: Modules and homomorphisms Projective modules Completely reducible modules Wedderbum rings Artinian rings Hereditary rings Dedekind domains Projective dimension Tensor products Local rings Polynomial rings: Skew polynomial rings Grothendieck groups Graded rings and modules Induced modules Syzygy theorem Patching theorem Serre conjecture Big projectives Generic flatness Nullstellensatz Injective modules: Injective modules Injective dimension Essential extensions Maximal ring of quotients Classical ring of quotients Goldie rings Uniform dimension Uniform injective modules Reduced rank Index.

A Course in Ring Theory

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    A Hardback by American Mathem American Mathem

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      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 9/30/2004 12:00:00 AM
      ISBN13: 9780821836804, 978-0821836804
      ISBN10: 0821836803

      Description

      Book Synopsis
      Suitable for an undergraduate first course in ring theory, this work discusses the various aspects of commutative and noncommutative ring theory. It begins with basic module theory and then proceeds to surveying various special classes of rings (Wedderbum, Artinian and Noetherian rings, hereditary rings and Dedekind domains.).

      Table of Contents
      Projective modules: Modules and homomorphisms Projective modules Completely reducible modules Wedderbum rings Artinian rings Hereditary rings Dedekind domains Projective dimension Tensor products Local rings Polynomial rings: Skew polynomial rings Grothendieck groups Graded rings and modules Induced modules Syzygy theorem Patching theorem Serre conjecture Big projectives Generic flatness Nullstellensatz Injective modules: Injective modules Injective dimension Essential extensions Maximal ring of quotients Classical ring of quotients Goldie rings Uniform dimension Uniform injective modules Reduced rank Index.

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