STAR-INVERTIBILITY AND t-FINITE CHARACTER IN INTEGRAL DOMAINS

Abstract

Abstract. Let A be an integral domain. We study new conditions on families of integral ideals of A in order to get that A is of t-finite character (i.e., each nonzero element of A is contained in finitely many t-maximal ideals). We also investigate problems connected with the local invertibility of ideals.

Integral Domains in Which Every Nonzero w-Flat Ideal Is w-Invertible

“…Recently, in [4], the authors introduced and studied the notion of a w-LPI domain; that is, an integral domain in which every nonzero w-locally principal ideal is w-invertible. (Relevant definitions and notations will be given in Section 1.2; and for more on w-LPI domains, the readers can refer to [5].) This is, the w-operation version of LPI domains.…”

Open Problems in Commutative Ring Theory

“…F. Halter-Koch gave independently another proof in the more general context of ideal systems [71]. Other contributions were made by M. Zafrullah in [111] and by C. A. Finocchiaro, G. Picozza and F. Tartarone in [41]. Following D. D. Anderson and M. Zafrullah [7], an integral domain D is called an LPI-domain if each locally principal nonzero ideal of D is invertible.…”

Stability and Clifford Regularity with Respect to Star Operations

“…We will use the fact that, for * of finite type, a Clifford * -regular domain has the * -local * -invertibility property (i.e., each ideal I such that I * R M is principal for all M ∈ * -Max(R) is * -invertible) [28,Lemma 4.4] and the following results from [19] (or from [13]). x ∈ R, any family of pairwise * -comaximal * -invertible * -ideals containing x is finite.…”