Prime ideals in decomposable lattices

2010/06/19 by Xinmin Lu, Lu, Xinmin, Dongsheng Liu +5 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Fuzzy and Soft Set Theory #Rings, Modules, and Algebras #math.CO

paper · pdf · doi:10.48550/arxiv.1006.3850

21 pages

arxiv created 2010/06/19 · arxiv updated 2010/06/22

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 a,b∈ L such that a=a\vee(a\wedge b), b=b\vee(a\wedge b) and a\wedge 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.

Cited by

• The structure of decomposable lattices determined by their prime ideals

Related

• The structure of decomposable lattices determined by their prime ideals
• Prime ideals and Noetherian properties in vector lattices
• Filters and ideals in pseudocomplemented posets
• Prime and primary ideals in characteristic one
• Minimal primes of ideals arising from conditional independence statements