Principally Dual Stable Modules

Abstract

Another generalization of fully d-stable modules, in this paper was introduced. A module is principally d-stable if every cyclic submodule of it is d-stable. Quasi-projective principally d-stable module is fully d-stable. For  finitely generated modules over  Dedekind domains the two concepts (full and principal) d-stability of modules coincide. For regular modules over commutative rings, principal d-stability of modules is equivalent to commutativity and full d-stability of there endomorphism rings.

Keywords: fully( principally) d-stable module; quasi-projective, duo, regular module; Dedekind domain; endomorphism ring; hollow module; exchange property.