On uniformly 1-absorbing primary ideals

Abstract

In this article, we introduce the concept of uniformly 1-absorbing primary ideal which is a generalization of uniformly primary ideal. Let R be a commutative ring with a unity and P be a proper ideal of R. P is said to be a uniformly 1-absorbing primary ideal if there exists N is an element of N such that whenever xyz is an element of P for some nonunits x, y, z is an element of R, we have either xy is an element of P or z(N) is an element of P. The smallest aforementioned N is an element of N is called the order of P and denoted by ord(R)(P) = N. In addition to giving many properties of uniformly 1-absorbing primary ideals, we investigate the relationship between uniformly 1-absorbing primary ideals and other classical ideals such as uniformly primary ideals and 1-absorbing primary ideals.