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.

Supported by King Fahd University of Petroleum and Minerals under Research Grant No. RG1328.