Rings, Modules, and Closure Operations

Jesse Elliott (Autor)

Buch | Softcover

XXIV, 490 Seiten

2021 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-24403-3 (ISBN)

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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.

lt;p>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.

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.

"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)

Erscheinungsdatum	25.12.2020
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	XXIV, 490 p. 7 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	783 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Schlagworte	Algebraic Structures • closure ideal and submodules • closure operations • Commutative Rings • divisorial nuclei • finitary nuclei • functorial systems • Integral Domains • multiplicative ideal theory • Ordered algebraic structures • polynomial rings • preradical theories • pretorsion theories • Prufer extensions • ring operations • semiprime operations • semistar operations • Star operations
ISBN-10	3-030-24403-2 / 3030244032
ISBN-13	978-3-030-24403-3 / 9783030244033
Zustand	Neuware