When Are Graded Rings Graded S -Noetherian Rings

Dong Kyu Kim and Jung Wook Lim
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Dong Kyu Kim: 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, 1-11

Abstract: Let Γ be a commutative monoid, R = ? α ∈ Γ R α a Γ -graded ring and S a multiplicative subset of R 0 . We define R to be a graded S -Noetherian ring if every homogeneous ideal of R is S -finite. In this paper, we characterize when the ring R is a graded S -Noetherian ring. As a special case, we also determine when the semigroup ring is a graded S -Noetherian ring. Finally, we give an example of a graded S -Noetherian ring which is not an S -Noetherian ring.

Keywords: S -Noetherian ring; graded S -Noetherian ring; S -finite algebra; Cohen type theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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