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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 63, Issue 6

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Prime, irreducible elements and coatoms in posets

Weifeng Zhou
  • College of Mathematics and Econometrics, Hunan University, Hunan Changsha, China
  • School of Sciences, Nanchang Institute of Technology, Jiangxi Nanchang, China
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/ Qingguo Li / Lankun Guo
Published Online: 2013-12-29 | DOI: https://doi.org/10.2478/s12175-013-0163-9

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.

MSC: Primary 06A06; Secondary 06A11, 06C15

Keywords: Boolean poset; prime element; irreducible element; atom

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About the article

Published Online: 2013-12-29

Published in Print: 2013-12-01


Citation Information: Mathematica Slovaca, Volume 63, Issue 6, Pages 1163–1178, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-013-0163-9.

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© 2013 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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