On Nonnil- S -Noetherian Rings

Min Jae Kwon and Jung Wook Lim
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Min Jae Kwon: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 41566, Korea
Jung Wook Lim: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 41566, Korea

Mathematics, 2020, vol. 8, issue 9, 1-14

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.

Keywords: nonnil-S-Noetherian ring; S-Noetherian ring; S-finite ideal; SFT ring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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