Rings, Modules, and Closure Operations

AvJesse Elliott

Inbunden, Engelska, 2019

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2019-12-11
Mått:155 x 235 x 34 mm
Vikt:939 g
Format:Inbunden
Språk:Engelska
Serie:Springer Monographs in Mathematics
Antal sidor:490
Upplaga:19001
Förlag:Springer Nature Switzerland AG
ISBN:9783030244002

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

“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)

Innehållsförteckning

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.