Chain Conditions in Commutative Rings

1. Auflage 2022
ISBN: 978-3-031-09897-0
Verlag: Springer International Publishing

Buch, Englisch, 522 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 963 g

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Benhissi, Ali

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe

Inhaltsverzeichnis

- 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.

Über Autor(innen)

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.”