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On Nonnil- S -Noetherian Rings

Author

Listed:
  • 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)

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.

Suggested Citation

  • Min Jae Kwon & Jung Wook Lim, 2020. "On Nonnil- S -Noetherian Rings," Mathematics, MDPI, vol. 8(9), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1428-:d:404127
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