Description
Book SynopsisThis book gathers, in a beautifully structured way, recent findings on chain conditions in commutative algebra that were previously only available in papers. The majority of chapters are self-contained, and all include detailed proofs, a wealth of examples and solved exercises, and a complete reference list. The topics covered include S-Noetherian, S-Artinian, Nonnil-Noetherian, and Strongly Hopfian properties on commutative rings and their transfer to extensions such as polynomial and power series rings, and more. Though primarily intended for readers with a background in commutative rings, modules, polynomials and power series extension rings, the book can also be used as a reference guide to support graduate-level algebra courses, or as a starting point for further research.
Trade Review“A unique one-of-a-kind book that brings together a wide array of state-of-the-art results around the generalized notions of noetherianness in rings. All in all, I identify it as a well-written readable book which experts will enjoy having on their shelves.” (Hossein Faridian, Mathematical Reviews, September, 2023)
“Each chapter of the book is followed by many interesting solved exercices and a bibliography. This book is nicely written and is worth reading. It is of great interest for the beginners or experts in the field of commutative rings.” (Sana Hizem, zbMATH 1504.13001, 2023)
Table of Contents- Preface.- S-Noetherian Modules and Rings.- S-Artininian Rings and Modules.- Almost Principal Polynomial Rings.- The SFT and t-SFT rings.- Nonnil-Noetherian Rings.- Strongly Hopfian, Endo-Noetherian and Isonoetherian Rings.- Index.
