Some Structure Theorems for Atomistic Algebraic Lattices

被引：0

作者：

S. Radeleczki

机构：

[1] University of Miskolc,Institute of Mathematics

来源：

Acta Mathematica Hungarica | 2000年 / 86卷

关键词：

Direct Product; Structure Theorem; Congruence Lattice; Algebraic Lattice; Irreducible Lattice;

D O I：

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中图分类号：

学科分类号：

摘要：

We prove that any atomistic algebraic lattice is a direct product of subdirectly irreducible lattices iff its congruence lattice is an atomic Stone lattice. We define on the set A(L) of all atoms of an atomistic algebraic lattice L a relation R as follows: for a, bA(L), (a, b) R ⇔ θ(0, a) ∧ θ(0, b) ≠ ▵Con L. We prove that Con L is a Stone lattice iff R is transitive and we give a characterization of Cen (L) using R. We also give a characterization of weakly modular atomistic algebraic lattices.

引用

页码：1 / 15

页数：14

共 6 条

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[4]

Schmidt E. T.(1995)Direct decompositions of atomistic algebraic lattices Algebra Universalis 33 127-135

[5]

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