Studying the Krull Dimension of Finite Lattices Under the Prism of Matrices

被引：5

作者：

Dube, T. ^{[1
]}

Georgiou, D. N. ^{[2
]}

Megaritis, A. C. ^{[3
]}

Sereti, F. ^{[2
]}

机构：

[1] Univ South Africa, Dept Math Sci, POB 392, ZA-0003 Pretoria, South Africa

[2] Univ Patras, Dept Math, Patras 26500, Greece

[3] Technol Educ Inst Western Greece, Dept Accounting & Finance, Mesolongion 30200, Greece

来源：

FILOMAT | 2017年 / 31卷 / 10期

关键词：

Krull dimension; finite poset; finite lattice; incidence matrix; order-matrix; join prime elements; prime filters; height;

D O I：

10.2298/FIL1710901D

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Krull dimension of a finite lattice (X, <=) is equal to the height of the poset of join prime elements of X minus 1. To every partially ordered set we assign an order-matrix, and we use these order-matrices to characterize the join prime elements of finite lattices. In addition, we present a reduction algorithm for the computation of the height of a finite poset. The algorithm is based on the concept of the incidence matrix. Our main objective, ultimately, is to use these processes to calculate the Krull dimension of any given finite lattice.

引用

页码：2901 / 2915

页数：15