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Module theory : endomorphism rings and direct sum decompositions in some classes of modules /

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The purpose of this expository monograph is three-fold. First, the solution of a problem posed by Wolfgang Krull in 1932 is presented. He asked whether what is now called the 'Krull-Schmidt Theorem' holds for artinian modules. A negative answer was published only in 1995 by Facchini, Herbe...

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Bibliographic Details
Main Author: Facchini, Alberto (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Basel : Springer, [2012]
Series:Modern Birkhäuser classics.
Subjects:
Modules (Algebra)
Endomorphism rings.
Direct sum decompositions.
Mathematics.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Basic concepts
  • The Krull-Schmidt-Remak-Azumaya Theorem
  • Semiperfect rings
  • Semilocal rings
  • Serial rings
  • Quotient rings
  • Krull dimension and serial rings
  • Krull-Schmidt fails for finitely generated modules and Artinian modules
  • Biuniform modules
  • [Sigma]-pure-injective modules and Artinian modules
  • Open problems.