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arXiv · 1006.3853

The structure of decomposable lattices determined by their prime ideals

Xinmin Lu·Dongsheng Liu·Zhinan Qi·Hourong Qin
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Abstract

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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Xinmin Lu, Dongsheng Liu, Zhinan Qi, Hourong Qin. 2010-06-19. The structure of decomposable lattices determined by their prime ideals. https://arxiv.org/abs/1006.3853

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