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This 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.
List 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.
About the author
Ali Benhissi is a Professor of Mathematics at the University of Monastir, Tunisia. He received his PhD in Mathematics from the University of Provence, France, in 1988, and completed his State thesis at the University of Tunis, Tunisia, in 1996. He began his career as an Assistant at the University of Monastir, Tunisia, before advancing to Maitre Assistant and Maitre de Conférences, and is now a Full Professor. Dr. Benhissi has published more than 40 research papers on various aspects of commutative algebra and one book: "Les anneaux de séries formelles."
Report
"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)
