Ideal Theory of Commutative Rings and Monoids / by Franz Halter-Koch ; edited by Alfred Geroldinger, Andreas Reinhart.

Format:

Book

Author/Creator:

Halter-Koch, Franz, 1944-2023, Author.

Contributor:

Geroldinger, Alfred, Editor.

Reinhart, Andreas (Researcher), Editor.

Series:

Lecture Notes in Mathematics, 1617-9692 ; 2368

Language:

English

Subjects (All):

Commutative algebra.

Commutative rings.

Group theory.

Commutative Rings and Algebras.

Group Theory and Generalizations.

Local Subjects:

Commutative Rings and Algebras.

Group Theory and Generalizations.

Physical Description:

1 online resource (X, 282 p. 1 illus.)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

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.

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.

ISBN:

3-031-88878-2

OCLC:

1524421193