On z0-ideals and annihilator ideals

Taherifar, Ali

doi:10.22055/jamm.2026.51789.2469

On z0-ideals and annihilator ideals

Document Type : Original Paper

Author

Ali Taherifar

10.22055/jamm.2026.51789.2469

Abstract

For a ∈ R, let Pa denote the intersection of all minimal prime
ideals of R containing a. An ideal I of a ring R is called a z◦-ideal if Pa ⊆ I
for all a ∈ I. In this paper, we first investigate the class of z
◦-ideals innon-commutative rings. We provide characterizations of z◦-ideals in 2-by-2
generalized triangular matrix rings, full and upper triangular matrix rings, and
semiprime rings. Next, we explore new properties of the lattice rAnn(id(R)),
the set of right annihilator ideals of R. We prove that rAnn(id(R)) forms
an algebraic frame when R is semiprime and a coherent frame when R is a
reduced ring. Furthermore, we characterize the smallest (resp., largest) right
annihilator ideal containing (resp., contained in) an ideal I of an SA-ring R.

Keywords

SA-ring

IN-ring

z◦-ideal

Annihilator ideal

Semiprime ring

Frame

Subjects