Monomial conditions on rings

Abstract

Drazin introduced the notion ofpivotal monomial, a condition on the evaluations of monomials in a ring, and characterized simple artinian rings as those primitive rings which have pivotal monomials. In this paper we consider monomial conditions related to pivotal monomials. The two major results are a characterization of prime Goldie rings in terms of pivotal monomials, and a characterization of the socle of a primitive ring in terms of generalized pivotal monomials.