The structure of decomposable lattices determined by their prime ideals

Details The structure of decomposable lattices determined by their prime ideals The structure of decomposable lattices determined by their prime ideals

2010-06-19

arxiv.org/abs/1006.3853v1

Mathematics

Group Theory

21 pages

Scientific paper

A distributive lattice $L$ with minimum element $0$ is called decomposable if $a$ and $b$ are not comparable elements in $L$ then 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 study the structure of decomposable lattices determined by their prime ideals. The properties for five special decomposable lattices are derived.

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