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BY-NC-ND 3.0 license Open Access Published by De Gruyter December 29, 2013

Prime, irreducible elements and coatoms in posets

  • Weifeng Zhou EMAIL logo , Qingguo Li and Lankun Guo
From the journal Mathematica Slovaca

Abstract

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.

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Published Online: 2013-12-29
Published in Print: 2013-12-1

© 2013 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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