1. ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS

M. Abedi

Volume 7, Issue 2 , Winter and Spring 2020, , Pages 257-269

Abstract
  We study primary ideals of the ring $\mathcal{R}L$ of real-valued continuous functions on a completely regular frame $L$. We observe that prime ideals and primary ideals coincide in a $P$-frame. It is shown that every primary ideal in $\mathcal{R}L$ is contained in a unique maximal ideal, and an ideal ...  Read More

2. INTERSECTION OF ESSENTIAL IDEALS IN THE RING OF REAL-VALUED CONTINUOUS FUNCTIONS ON A FRAME

A. A. Estaji; A. Gh. Karimi Feizabadi; M. Abedi

Volume 5, Issue 2 , Winter and Spring 2018, , Pages 149-161

Abstract
  A frame $L$ is called {\it coz-dense} if $\Sigma_{coz(\alpha)}=\emptyset$ implies $\alpha=\mathbf 0$. Let $\mathcal RL$ be the ring of real-valued continuous functions on a coz-dense and completely regular frame $L$. We present a description of the socle of the ring $\mathcal RL$ based on minimal ideals ...  Read More