Prime ideals in decomposable lattices

Abstract

A distributive lattice $L$ with minimum element $0$ is called decomposable lattice if $a$ and $b$ are not comparable elements in $L$ there exist $\overline{a},\overline{b}\in L$ such that $a=\overline{a}\vee (a\wedge b),b=\overline{b}\vee (a\wedge b)$ and $\overline{a}\wedge \overline{b}=0$. The main purpose of this paper is to investigate prime ideals, minimal prime ideals and special ideals of a decomposable lattice. These are keys to understand the algebraic structure of decomposable lattices.

21 pages

References in corpus (1)

• The structure of decomposable lattices determined by their prime ideals

Cited by in corpus (1)

• The structure of decomposable lattices determined by their prime ideals