Prime, irreducible elements and coatoms in posets

Mathematica Slovaca

Lankun Guo¹  Weifeng Zhou¹  Qingguo Li¹ 

关键词: Boolean poset;    prime element;    irreducible element;    atom;   

DOI  :  10.2478/s12175-013-0163-9

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

In this paper, some properties of prime elements, pseudoprime elements, irreducible elements and coatoms in posets are investigated. We show that the four kinds of elements are equivalent to each other in finite Boolean posets. Furthermore, we demonstrate that every element of a finite Boolean poset can be represented by one kind of them. The example presented in this paper indicates that this result may not hold in every finite poset, but all the irreducible elements are proved to be contained in each order generating set. Finally, the multiplicative auxiliary relation on posets and the notion of arithmetic poset are introduced, and some properties about them are generalized to posets.

【 授权许可】

Unknown