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.
Author(s): Jesse Elliott
Series: Springer Monographs in Mathematics
Publisher: Springer
Year: 2019
Language: English
Pages: 512
Front Matter ....Pages i-xxiv
Preliminaries (Jesse Elliott)....Pages 1-12
Introductory Survey of Multiplicative Ideal Theory (Jesse Elliott)....Pages 13-62
Semistar Operations on Commutative Rings (Jesse Elliott)....Pages 63-180
Semistar Operations on Commutative Rings: Local Methods (Jesse Elliott)....Pages 181-290
Semiprime, Star, and Semistar Operations on Commutative Rings (Jesse Elliott)....Pages 291-361
Noncommutative Rings and Closure Operations on Submodules (Jesse Elliott)....Pages 363-440
Closure Operations and Nuclei (Jesse Elliott)....Pages 441-476
Back Matter ....Pages 477-490
