Work

Some remarks on $S$-Noetherian modules

Year: 2025

Type: article

Abstract: UDC 512.5 We study several properties and applications of the $S$-Noetherian rings and modules. It is proved that an $S$-Artinian ring is $S$-Noetherian provided that $S$ contains no zero divisors of the module. Furthermore, it is shown that associated primes exist in modules over the $S$-Noetherian rings and the major part of notions of associated prime ideals coincide over the $S$-Noetherian rings. We also extend the classical Krull's intersection theorem for $S$-Noetherian rings. Moreover, we provide a characterization of the $S$-Noetherian modules in terms of the $G$-graded $S$-Noetherian modules.

Source: Ukrains’kyi Matematychnyi Zhurnal

DOI: 10.3842/umzh.v77i1.7907

Authors: Ajim Uddin Ansari, Sanjeev Kumar Maurya, B. K. Sharma

Institutions: University of Allahabad, Galgotias University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4408133445

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