Centrally essential group algebras and classical rings of fractions (Q2062091)

A ring \(R\) with center \(C(R)\) is said to be centrally essential if the module \(R_{C(R)}\) is an essential extension of the module \(C(R)_{C(R)}\). In this case, for every non-zero element \(a\) of \(R\) there exist two non-zero central elements \(x, y\) with \(ax = y\). The main result of the paper is Theorem 1: Any centrally essential group algebra over any field has the two-sided classical ring of fractions. In addition, the group algebra over a field is centrally essential if and only if it has the classical right ring of fractions which is a centrally essential ring.