Commutative Ring Theory

9 Some Locally Trivial Star-Theoretic Properties of Integral Domains

David E. Dobbs* Department of Mathematics University of Tennessee Knoxville, Tennessee 37996-1300 U.S.A.

Muhammad Zafrullah Department of Mathematics Winthrop College Rock Hill, South Carolina 29733 U.S.A.

ABSTRACT. Using the t- and the v-operations, we introduce two properties, dubbed (T) and (V), that hold for all quasi-local domains and for some special non-quasi-local domains. We show that a non-quasi-local domain D satisfies (T) (resp., (V)) if and only if D is a t-linkative (resp., a t-linkative H-) domain. Upshots include new characterizations of non-quasi-local Prüfer domains and non-quasi-local Dedekind domains.

Throughout this note, D denotes a (commutative integral) ...