Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 404-418 |
| Number of pages | 15 |
| Journal | New York Journal of Mathematics |
| Volume | 24 |
| State | Published - 9 Jul 2018 |
Bibliographical note
Funding 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.
Publisher Copyright:
© 2018, University at Albany. All rights reserved.
Keywords
- Noetherian domain
- T-C-ideal
- T-basic ideal
- T-ideal
- T-invertibility
- T-operation
- T-reduction
- V-operation
- W-operation
ASJC Scopus subject areas
- Mathematics (all)