ON QUASI MAXIMAL IDEALS OF COMMUTATIVE RINGS

Abstract

Let R be a commutative ring with 1 =? 0. A proper ideal I of R is said to be a quasi maximal ideal if for every a E R - I, either I + Ra = R or I + Ra is a maximal ideal of R. This class of ideals lies between 2-absorbing ideals and maximal ideals which is different from prime ideals. In addition to give fundamental properties of quasi maximal ideals, we characterize principal ideal UN-rings with V02 = (0), direct product of two fields, and Noetherian zero dimensional modules in terms of quasi maximal ideals.