This paper studies t-reductions and t-integral closure of ideals in Noetherian domains. The main objective is to establish satisfactory t-analogues for well-known results in the literature on reductions and integral closure of ideals in Noetherian rings. Namely, Section 2 investigates t-reductions of ideals subject to t-invertibility and localization in Noetherian domains. Section 3 investigates the t-integral closure of ideals and its correlation with t-reductions in Noetherian domains of Krull dimension one. Section 4 studies the t-analogue of Hays’ classic notion of C-ideal and its correlation to the integral closure.
|Number of pages||15|
|Journal||New York Journal of Mathematics|
|State||Published - 9 Jul 2018|
Bibliographical noteFunding Information:
Received October 19, 2017. 2010 Mathematics Subject Classification. 13A15, 13A18, 13F05, 13G05, 13C20. Key words and phrases. Noetherian domain, t-operation, t-ideal, t-invertibility, t-reduction, t-basic ideal, t-C-ideal, v-operation, w-operation. Supported by King Fahd University of Petroleum & Minerals under Research Grant # RG1328.
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- Noetherian domain
- T-basic ideal
ASJC Scopus subject areas
- Mathematics (all)