On n-primly ideals

Abstract

An ideal I is primal over a commutative ring R with non zero identity if the set of all elements that are not prime to I, forms an ideal of R. This definition was introduced by Ladislas Fuchs in 1950. In this paper, we define an ideal I over a commutative ring R with non zero identity to be n-primly if the set of all elements that are not n-primary to I, forms an ideal of R. But first we introduced the concepts of n-primary elements to an ideal, n-adjoint sets for an ideal, uniformly not n-primary sets for an ideal, n-primly ideals and uniformly n-primly ideals. We study the previous concepts in details illustrated by several examples. We also study the relation between several sets like n-adjoint sets for an ideal, n-adjoint sets for an ideal and the adjoint set for this ideal, sets that are not n-primary for an ideal and uniformly not n-primary sets for this ideal. Also we investigate the relation between some ideals like uniformly n-primly ideals and n-primly ideals, primary ideals and n-primly ideals over a commutative ring with identity