Distributive invariant centrally essential rings

Abstract

In recent years, centrally essential rings have been intensively studied in ring theory. In particular, they find applications in homological algebra, group rings, and the structural theory of rings. The class of essentially central rings strongly extends the class of commutative rings. For such rings, a number of recent papers contain positive answers to some important questions from ring theory that previously had positive answers for commutative rings and negative answers in the general case. This work is devoted to a similar topic. A familiar description of right Noetherian, right distributive centrally essential rings is generalized on a larger class of rings. Let [Formula: see text] be a ring with prime radical [Formula: see text]. It is proved that [Formula: see text] is a right distributive, right invariant centrally essential ring and [Formula: see text] is a finitely generated right ideal such that the factor-ring [Formula: see text] does non contain an infinite direct sum of nonzero ideals if and only if [Formula: see text], where every ring [Formula: see text] is either a commutative Prüfer domain or an Artinian uniserial ring. The studies of Tuganbaev are supported by Russian scientific foundation project 22-11-00052.