Prime \(\alpha\)-ideals in a 0-distributive lattice
type: Item
instance of: scholarly article
title: Prime \(\alpha\)-ideals in a 0-distributive lattice
zbMATH Open document ID: 0595.06010
author: C. Jayaram
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: A lattice L with 0 is said to be 0-distributive if a,b,c\(\in L\), \(a\wedge b=0=a\wedge c\) implies \(a\wedge (b\vee c)=0\). An ideal I of L is called an \(\alpha\)-ideal if \(x\in I\Rightarrow (x)^{**}\subseteq I\). The author introduces a topology on the set of all prime \(\alpha\)-ideals of a 0-distributive lattice L. He proves that the topology is \(T_ 0\) and that the compact open sets form a base for the open sets. He also derives some other properties of the topology and uses them to obtain some equivalent conditions for the space of minimal prime ideals of L with the hull kernel topology to be compact and discrete.
Mathematics Subject Classification ID: 06B10
Mathematics Subject Classification ID: 06B30
Mathematics Subject Classification ID: 54D10
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 3957186
zbMATH Keywords: prime \(\alpha \) -ideals
zbMATH Keywords: 0-distributive lattice
zbMATH Keywords: space of minimal prime ideals
zbMATH Keywords: hull kernel topology
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3957186