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Rings, Modules, and Closure Operations

  • Book
  • © 2019

Overview

Authors:
  1. Jesse Elliott

    1. Department of Mathematics, California State University, Channel Islands, Camarillo, USA

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  • 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

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xxiv
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  2. Preliminaries

    • Jesse Elliott
    Pages 1-12

  3. Introductory Survey of Multiplicative Ideal Theory

    • Jesse Elliott
    Pages 13-62

  4. Semistar Operations on Commutative Rings

    • Jesse Elliott
    Pages 63-180

  5. Semistar Operations on Commutative Rings: Local Methods

    • Jesse Elliott
    Pages 181-290

  6. Semiprime, Star, and Semistar Operations on Commutative Rings

    • Jesse Elliott
    Pages 291-361

  7. Noncommutative Rings and Closure Operations on Submodules

    • Jesse Elliott
    Pages 363-440

  8. Closure Operations and Nuclei

    • Jesse Elliott
    Pages 441-476

  9. Correction to: Rings, Modules, and Closure Operations

    • Jesse Elliott
    Pages C1-C3

  10. Back Matter

    Pages 477-490
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Keywords

About this book

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

“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)

Authors and Affiliations

  • Department of Mathematics, California State University, Channel Islands, Camarillo, USA

    Jesse Elliott

About the author

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.

Bibliographic Information

  • Book Title: Rings, Modules, and Closure Operations

  • Authors: Jesse Elliott

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-24401-9

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-24400-2Published: 11 December 2019

  • Softcover ISBN: 978-3-030-24403-3Published: 17 January 2021

  • eBook ISBN: 978-3-030-24401-9Published: 30 November 2019

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XXIV, 490

  • Number of Illustrations: 7 b/w illustrations

  • Topics: Commutative Rings and Algebras

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