可換環とモノイドのイデアル理論 Ideal Theory of Commutative Rings and Monoids

著者名：Halter-Koch, Franz/Geroldinger, Alfred (EDT)/Reinhart, Andreas (EDT)

Springer（2025/05/13発売）

• 言語：ENG
• ISBN：9783031888779
• eISBN：9783031888786

Description

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.

Table of Contents

- 1. Basic Monoid Theory.- 2. The Formalism of Module and Ideal Systems.- 3. Prime and Primary Ideals and Noetherian Conditions.- 4. Invertibility, Cancellation and Integrality.- 5. Arithmetic of Cancellative Mori Monoids.- 6. Ideal Theory of Polynomial Rings.