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Ideal theory of commutative rings and monoids

Record Type:	Electronic resources : Monograph/item
Title/Author:	Ideal theory of commutative rings and monoidsby Franz Halter-Koch ; edited by Alfred Geroldinger, Andreas Reinhart.
Author:	Halter-Koch, Franz.
other author:	Geroldinger, Alfred.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	x, 282 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Monoids.
Online resource:	https://doi.org/10.1007/978-3-031-88878-6
ISBN:	9783031888786$q(electronic bk.)

Ideal theory of commutative rings and monoids
Halter-Koch, Franz.

Ideal theory of commutative rings and monoids[electronic resource] /by Franz Halter-Koch ; edited by Alfred Geroldinger, Andreas Reinhart. - Cham :Springer Nature Switzerland :2025. - x, 282 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23681617-9692 ;. - Lecture notes in mathematics ;2035..

- 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.

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.

ISBN: 9783031888786$q(electronic bk.)

Standard No.: 10.1007/978-3-031-88878-6doiSubjects--Topical Terms:

764483
Monoids.

LC Class. No.: QA169

Dewey Class. No.: 512.55

Ideal theory of commutative rings and monoids
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245 1 0 $a Ideal theory of commutative rings and monoids $h [electronic resource] / $c by Franz Halter-Koch ; edited by Alfred Geroldinger, Andreas Reinhart.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a x, 282 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2368
505 0 $a - 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.
520 $a 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.
650 0 $a Monoids. $3 764483
650 0 $a Commutative rings. $3 237116
650 1 4 $a Commutative Rings and Algebras. $3 274057
650 2 4 $a Group Theory and Generalizations. $3 274819
700 1 $a Geroldinger, Alfred. $3 239605
700 1 $a Reinhart, Andreas. $3 991603
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830 0 $a Lecture notes in mathematics ; $v 2035. $3 557764
856 4 0 $u https://doi.org/10.1007/978-3-031-88878-6
950 $a Mathematics and Statistics (SpringerNature-11649)