Rings, Modules, and Closure Operations
1st Edition
Published on 11. December 2019
Book
Hardback
XXIV, 490 pages
978-3-030-24400-2 (ISBN)
Description
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.
Reviews / Votes
"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)
More details
Series
Edition
1st ed. 2019
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Primary & secondary/elementary & high school
Illustrations
7 s/w Abbildungen
XXIV, 490 p. 7 illus.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 34 mm
Weight
939 gr
ISBN-13
978-3-030-24400-2 (9783030244002)
DOI
10.1007/978-3-030-24401-9
Schweitzer Classification
Other editions
Additional editions
Jesse Elliott
Rings, Modules, and Closure Operations
Book
01/2021
Springer
€128.39
Shipment within 7-9 days
Jesse Elliott
Rings, Modules, and Closure Operations
E-Book
11/2019
Springer
€117.69
Available for download
Person
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.
Content
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.