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Commutative Rings

Editat de John Lee
en Limba Engleză Hardback – 8 dec 2009
Commutative rings are a branch of abstract algebra that deals with the multiplication operation. This book examines the question, given any positive integer n, is there a commutative ring with identity that has n zero-divisions? This question is examined in stages through looking at local rings, reduced rings and finally commutative rings in general. In addition, several themes pertaining to the classification of minimal ring extensions are described. Some recent and new results on linear systems theory over commutative rings are also looked at. Finally, this book gives a brief history and summary of the active area of asymptotic stability of associated or attached prime ideals. Some of the old and new results about the asymptotic properties of associated and attached prime ideals related to injective, projective or flat modules, are discussed.
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Specificații

ISBN-13: 9781606926147
ISBN-10: 1606926144
Pagini: 127
Ilustrații: Illustrations
Dimensiuni: 188 x 265 x 15 mm
Greutate: 0.52 kg
Editura: Nova Science Publishers Inc

Cuprins

Preface; Jonsson Modules over Commutative Rings; Counting Zero-Divisors; Recent Progress on Minimal Ring Extensions and Related Concepts; Commutative Algebra Applied to Stabilization Problems for Systems over Rings; Asymptotic Behavior of Associated or Attached Prime Ideals of Certain Ext-modules and Tor-modules; Linear Algebra over Commutative Rings applied to Control Theory; A Characterization of Commutative Clean Rings; Jordan Automorphisms of Certain Jordan Matrix Algebra Over Commutative Rings; Index.