Some results concerning uniformly (1-absorbing) primary ideals

Abstract

Let R be a commutative ring with 1 not equal 0. A proper ideal I of R is said to be a uniformly 1-absorbing primary if there exits a fixed n is an element of & Nopf; and whenever abc is an element of I for some nonunits a,b,c is an element of R then ab is an element of I or c(n) is an element of I. In addition to give various properties of uniformly 1-absorbing primary ideals, we characterize some important classes of rings such as von Neumann regular rings, UN-rings, nonlocal rings, fields and divided rings in terms of uniformly 1-absorbing primary ideals. Also, we investigate uniformly primary ideals and uniformly 1-absorbing primary ideals of amalgamated algebras R & bowtie;(f)J.