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Rings, Modules, and Closure Operations

  • Jesse Elliott
Book

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

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Jesse Elliott
    Pages 1-12
  3. Jesse Elliott
    Pages 63-180
  4. Jesse Elliott
    Pages 441-476
  5. Back Matter
    Pages 477-490

About this book

Introduction

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.

Keywords

ring operations closure operations algebraic structures ordered algebraic structures multiplicative ideal theory integral domains semistar operations commutative rings polynomial rings Prufer extensions semiprime operations star operations closure ideal and submodules functorial systems preradical theories pretorsion theories divisorial nuclei finitary nuclei

Authors and affiliations

  • Jesse Elliott
    • 1
  1. 1.Department of MathematicsCalifornia State University, Channel IslandsCamarilloUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-24401-9
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-24400-2
  • Online ISBN 978-3-030-24401-9
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site