Rings, Modules, and Closure Operations

• Main Author: Elliott, Jesse (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Springer Monographs in Mathematics,
• Subjects: Commutative algebra.; Commutative rings.; Commutative Rings and Algebras.

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...

Table of 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.