Ideal Theory of Commutative Rings and Monoids: 2368 (Lecture Notes in Mathematics, 2368) - Softcover

Halter-Koch, Franz

Softcover

ISBN 10: 3031888774 ISBN 13: 9783031888779

Publisher: Springer, 2025

Synopsis

This book offers a concise treatment of multiplicative ideal theory in the language of multiplicative monoids. It presents a systematic development of the theory of weak ideal systems and weak module systems on arbitrary commutative monoids. Examples of monoids that are investigated include, but are not limited to, Mori monoids, Laskerian monoids, Prüfer monoids and Krull monoids. An in-depth study of various constructions from ring theory is also provided, with an emphasis on polynomial rings, Kronecker function rings and Nagata rings. The target audience is graduate students and researchers in ring and semigroup theory.

About this title

About the Author

Franz Halter-Koch was professor emeritus at the University of Graz, Graz, Austria. He is the author of Ideal Systems (Marcel Dekker,1998), Quadratic Irrationals (CRC, 2013), An Invitation to Algebraic Numbers and Algebraic Functions (CRC Press, 2020), Class Field Theory and L-Functions (CRC 2022), and co-author of Non-Unique Factorizations (CRC 2006). He passed away at the end of 2023, just before finalizing this monograph.

Alfred Geroldinger is professor at the University of Graz, Graz, Austria. He has published more than 100 research papers in commutative algebra and additive combinatorics. He is co-author of Non-Unique Factorizations (CRC 2006) and of Combinatorial Number Theory and Additive Group Theory (Birkhäuser 2009).

Andreas Reinhart is a researcher at the University of Graz, Graz, Austria. He has published about 25 research papers in commutative algebra and algebraic number theory.

From the Back Cover

This book offers a concise treatment of multiplicative ideal theory in the language of multiplicative monoids. It presents a systematic development of the theory of weak ideal systems and weak module systems on arbitrary commutative monoids. Examples of monoids that are investigated include, but are not limited to, Mori monoids, Laskerian monoids, Prüfer monoids and Krull monoids. An in-depth study of various constructions from ring theory is also provided, with an emphasis on polynomial rings, Kronecker function rings and Nagata rings. The target audience is graduate students and researchers in ring and semigroup theory.

Edition details

• Publisher: Springer
• Publication date: 2025
• Language: English
• ISBN 10: 3031888774
• ISBN 13: 9783031888779
• Binding: Paperback
• Number of pages: 292
• Editor: Geroldinger Alfred, Reinhart Andreas