arXiv subjects

Xinmin Lu

Publications and source records attributed to Xinmin Lu.

2 recordsLinked to original sources

arXiv2010

Prime ideals in decomposable lattices

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.

math.CO↗

arXiv2010

The structure of decomposable lattices determined by their prime ideals

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.

math.GR↗