Rings, Modules, and Closure Operations
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Beschreibung
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.
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.
Provides complete treatise about the most recent multiplicative ideal theory in commutative rings Includes a dependence chart for the various sections of the book Exercises included at the end of each section
Autor*in
Jesse Elliott
Themen in »Rings, Modules, and Closure Operations«
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
Stimmen zu »Rings, Modules, and Closure Operations«
“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)
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