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Rings, Modules, and Closure Operations de Jesse Elliott

Rings, Modules, and Closure Operations: Springer Monographs in Mathematics

Autor Jesse Elliott
en Limba Engleză Paperback – 17 ian 2021
This book presents a systematic exposition of the various applications of closure operations in commutative and noncommutative algebra.  In addition to further advancing multiplicative ideal theory, the book opens doors to the various uses of closure operations in the study of rings and modules, with emphasis on commutative rings and ideals. Several examples, counterexamples, and exercises further enrich the discussion and lend additional flexibility to the way in which the book is used, i.e., monograph or textbook for advanced topics courses. 
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Specificații

ISBN-13: 9783030244033
ISBN-10: 3030244032
Ilustrații: XXIV, 490 p. 7 illus.
Dimensiuni: 155 x 235 mm
Greutate: 0.72 kg
Ediția:1st ed. 2019
Editura: Springer International Publishing
Colecția Springer
Seria Springer Monographs in Mathematics

Locul publicării:Cham, Switzerland

Cuprins

Preface.- 0. Preliminaries.- 1. Introductory survey of multiplicative ideal theory.- 2. Semistar operations on commutative rings.- 3. Semistar operations on commutative rings: local methods.- 4. Extensions of commutative rings.- 5. Semiprime, star, and semistar operations on commutative rings.- 6. Closure operations on submodules over noncommutative rings.- 7. Appendix on Clusure operations and nuclei.- Bibliography.- Index.

Recenzii

“I am certain that there is a lot to learn here and that this text is a valuable contribution to the literature that did not previously exist.” (Geoffrey D. Dietz, Mathematical Reviews, March, 2021)

Notă biografică

Jesse Elliott is a professor of mathematics and philosophy at California State University Channel Islands. He received a PhD in Mathematics in 2003 from the University of California, Berkeley and received a BS in Mathematics in 1995 from the Massachusetts Institute of Technology. His areas of research are ring theory, number theory, and the philosophy of mathematics.

Textul de pe ultima copertă

This book presents a systematic exposition of the various applications of closure operations in commutative and noncommutative algebra.  In addition to further advancing multiplicative ideal theory, the book opens doors to the various uses of closure operations in the study of rings and modules, with emphasis on commutative rings and ideals. Several examples, counterexamples, and exercises further enrich the discussion and lend additional flexibility to the way in which the book is used, i.e., monograph or textbook for advanced topics courses.

Caracteristici

Provides complete treatise about the most recent multiplicative ideal theory in commutative rings Includes a dependence chart for the various sections of the book Exercises included at the end of each section