Ideals in distributive posets

被引：4

作者：

Batueva, Cyndyma ^{[1
]}

Semenova, Marina ^{[1
,2
]}

机构：

[1] Novosibirsk State Univ, Novosibirsk 630090, Russia

[2] Siberian Branch RAS, Sobolev Inst Math, Novosibirsk 630090, Russia

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2011年 / 9卷 / 06期

关键词：

Poset; Ideal; Prime ideal; Distributive; Normal; Completion; ORDERED SETS;

D O I：

10.2478/s11533-011-0075-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that any ideal in a distributive (relative to a certain completion) poset is an intersection of prime ideals. Besides that, we give a characterization of n-normal meet semilattices with zero, thus generalizing a known result for lattices with zero.

引用

页码：1380 / 1388

页数：9

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