On the Lattice of Z-ideals of a Commutative Ring

Authors

Oghenetega Ighedo, Chapman UniversityFollow
Warren Wm. McGovern, Florida Atlantic University

Document Type

Article

Publication Date

12-10-2019

Abstract

We prove that the lattice of z-ideals of a commutative ring with identity is a coherent frame. We characterize when it is a Yosida frame, and when it satisfies some projectability properties. We also characterize Hilbert rings in terms of ideals that arise naturally in this study. A ring with zero Jacobson radical is shown to be feebly Baer precisely when its frame of z-ideals is feebly projectable. Denote by ZId(A) the frame of z-ideals of a ring A. We show that the assignment A → ZId(A) is the object part of a functor CRngz → CohFrm, where CRngz designates the category whose objects are commutative rings with identity and whose morphisms are the ring homomorphisms that contract z-ideals to z-ideals.

Comments

This article was originally published in Topology and its Applications, volume 273, in 2020. https://doi.org/10.1016/j.topol.2019.106969

Recommended Citation

O. Ighedo & W.Wm. McGovern: On the lattice of z-ideals of a commutative ring. Topology and its Applications, 273 (2020) 106969. https://doi.org/10.1016/j.topol.2019.106969

Peer Reviewed

1

Copyright

Elsevier