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Commutative Rings: New Research
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Authors: John Lee 
Book Description:
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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Table of Contents:

Chapter 1. Jonsson Modules over Commutative Rings pp. 1-6
(Greg Oman, Dept. of Mathematics, The Ohio State Univ., Columbus, Ohio)

Chapter 2. Counting Zero-Divisors pp. 7-12
(Shane P. Redmond, Mathematics, Eastern Kentucky University)

Chapter 3. Recent Progress on Minimal Ring Extensions and Related Concepts pp. 13-38
(David E. Dobbs, Dept. of Mathematics, Univ. of Tennessee, Knoxville)

Chapter 4. Commutative Algebra Applied to Stabilization Problems for Systems over Rings pp. 39-51
(A. Saez-Schwedt, Dept. de Matematicas, Univ. de Leon, Campus de Vegazana, Leon, Spain)

Chapter 5. Asymptotic Behavior of Associated or Attached Prime Ideals of Certain Ext-modules and Tor-modules pp. 53-64
(K. Khasyarmanesh, F. Khosh-Ahang, it Ferdowsi Univ. of Mashhas, Dept. of Mathematics, Mashhad, Iran)

Chapter 6. ^Linear Algebra over Commutative Rings applied to Control Theory pp. 65-103
(Miguel V. Carriegos, Univ. de Le Spain)

Chapter 7. ^A Characterization of Commutative Clean Rings pp. 105-117
(Warren Wm. McGovern)

Chapter 8. ^Jordan Automorphisms of Certain Jordan Matrix Algebra Over Commutative Rings pp. 119-127
(Yao Ruiping, Dengyin Wang and Yanxia Zhao)


   Binding: Hardcover
   Pub. Date: 2009
   Pages: 131 pp.
   ISBN: 978-1-60692-614-7
   Status: AV
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
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Commutative Rings: New Research