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http://dx.doi.org/10.4134/BKMS.b191007

GRADED w-NOETHERIAN MODULES OVER GRADED RINGS  

Wu, Xiaoying (School of Mathematics and Science Sichuan Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.5, 2020 , pp. 1319-1334 More about this Journal
Abstract
In this paper, we study the basic theory of the category of graded w-Noetherian modules over a graded ring R. Some elementary concepts, such as w-envelope of graded modules, graded w-Noetherian rings and so on, are introduced. It is shown that: (1) A graded domain R is graded w-Noetherian if and only if Rg𝔪 is a graded Noetherian ring for any gr-maximal w-ideal m of R, and there are only finite numbers of gr-maximal w-ideals including a for any nonzero homogeneous element a. (2) Let R be a strongly graded ring. Then R is a graded w-Noetherian ring if and only if Re is a w-Noetherian ring. (3) Let R be a graded w-Noetherian domain and let a ∈ R be a homogeneous element. Suppose 𝖕 is a minimal graded prime ideal of (a). Then the graded height of the graded prime ideal 𝖕 is at most 1.
Keywords
Graded w-envelope of a module; graded w-exact sequence; graded finitely presented type module; graded w-Noetherian ring;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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