Chain Conditions in Commutative Rings

Ali Benhissi (Autor)

Buch | Hardcover

XI, 522 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-09897-0 (ISBN)

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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.

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 Conferences, 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 series formelles."

- 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.

"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)

Erscheinungsdatum	12.10.2022
Zusatzinfo	XI, 522 p. 31 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	961 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	almost principal • Amalgamation • chain conditions • Commutative Rings • Conditions • Nonnil-Noetherian • polynomials • power series • Rings • S-Artinian • S-Noetherian • Strongly Hopfian
ISBN-10	3-031-09897-8 / 3031098978
ISBN-13	978-3-031-09897-0 / 9783031098970
Zustand	Neuware