Rings, Modules, and Closure Operations [electronic resource] / by Jesse Elliott.

By: Elliott, Jesse [author.]Contributor(s): SpringerLink (Online service)Material type: Text

TextSeries: Springer Monographs in MathematicsPublisher: Cham : Springer International Publishing : Imprint: Springer, 2019Edition: 1st ed. 2019Description: XXIV, 490 p. 163 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783030244019Subject(s): Commutative algebra | Commutative rings | Commutative Rings and AlgebrasAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 512.44 LOC classification: QA251.3Online resources: Click here to access online

Contents:

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.

In: Springer eBooksSummary: 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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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.