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Prime, irreducible elements and coatoms in posets

In: Mathematica Slovaca, vol. 63, no. 6
Weifeng Zhou - Qingguo Li - Lankun Guo

Details:

Year, pages: 2013, 1163 - 1178
Keywords:
Boolean poset, prime element, irreducible element, atom
About article:
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.
How to cite:
ISO 690:
Zhou, W., Li, Q., Guo, L. 2013. Prime, irreducible elements and coatoms in posets. In Mathematica Slovaca, vol. 63, no.6, pp. 1163-1178. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0163-9

APA:
Zhou, W., Li, Q., Guo, L. (2013). Prime, irreducible elements and coatoms in posets. Mathematica Slovaca, 63(6), 1163-1178. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0163-9
About edition:
Published: 1. 12. 2013