Lasker–Noether Theorem for Nonnil-$ S $-Noetherian Rings

Siberian Mathematical Journal 2026

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Authors: T. Singh, S Nanda Kumar
DOI: 10.1134/s0037446626010222
Cited by: 0
References: 16

Abstract

We introduce the concept of $ S $ -primary decomposition for a commutative ring and show that if a ring admits an $ S $ -primary decomposition, then it admits a minimal $ S $ -primary decomposition. We establish the $ S $ -version of Krull’s intersection theorem by using the existence of $ S $ -primary decomposition in $ S $ -Noetherian domains. As the main result, we prove the Lasker–Noether theorem for nonnil- $ S $ -Noetherian rings, thereby extending the classical Lasker–Noether theorem.

Fields of Study & Subjects

Rings Modules and Algebras Commutative Algebra and Its Applications Algebraic Geometry and Number Theory

Publication details

Journal / source
Siberian Mathematical Journal
Volume
67
Issue
1
Pages
235–243
Publication date
1 January 2026
Language
EN