Author:
Kwon Min Jae,Lim Jung Wook
Abstract
Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite. In this paper, we study some properties of nonnil-S-Noetherian rings. More precisely, we investigate nonnil-S-Noetherian rings via the Cohen-type theorem, the flat extension, the faithfully flat extension, the polynomial ring extension, and the power series ring extension.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Cited by
8 articles.
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1. On φ-u-S-flat modules and nonnil-u-S-injective modules;Georgian Mathematical Journal;2024-01-02
2. On nonnil-very strong finite type commutative rings;São Paulo Journal of Mathematical Sciences;2023-12-21
3. S-injective modules;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2023-11-02
4. On a weak version of S-Noetherianity;Journal of Algebra and Its Applications;2023-06-15
5. Graded S-Noetherian Modules;International Electronic Journal of Algebra;2023-01-09