Relatively pseudocomplemented posets

Ivan Chajda; Helmut Länger

Mathematica Bohemica (2018)

  • Volume: 143, Issue: 1, page 89-97
  • ISSN: 0862-7959

Abstract

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We extend the notion of a relatively pseudocomplemented meet-semilattice to arbitrary posets. We show some properties of the binary operation of relative pseudocomplementation and provide some corresponding characterizations. We show that relatively pseudocomplemented posets satisfying a certain simple identity in two variables are join-semilattices. Finally, we show that every relatively pseudocomplemented poset is distributive and that the converse holds for posets satisfying the ascending chain condition and one more natural condition. Suitable examples are provided.

How to cite

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Chajda, Ivan, and Länger, Helmut. "Relatively pseudocomplemented posets." Mathematica Bohemica 143.1 (2018): 89-97. <http://eudml.org/doc/294284>.

@article{Chajda2018,
abstract = {We extend the notion of a relatively pseudocomplemented meet-semilattice to arbitrary posets. We show some properties of the binary operation of relative pseudocomplementation and provide some corresponding characterizations. We show that relatively pseudocomplemented posets satisfying a certain simple identity in two variables are join-semilattices. Finally, we show that every relatively pseudocomplemented poset is distributive and that the converse holds for posets satisfying the ascending chain condition and one more natural condition. Suitable examples are provided.},
author = {Chajda, Ivan, Länger, Helmut},
journal = {Mathematica Bohemica},
keywords = {relatively pseudocomplemented poset; join-semilattice; distributive poset},
language = {eng},
number = {1},
pages = {89-97},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Relatively pseudocomplemented posets},
url = {http://eudml.org/doc/294284},
volume = {143},
year = {2018},
}

TY - JOUR
AU - Chajda, Ivan
AU - Länger, Helmut
TI - Relatively pseudocomplemented posets
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 1
SP - 89
EP - 97
AB - We extend the notion of a relatively pseudocomplemented meet-semilattice to arbitrary posets. We show some properties of the binary operation of relative pseudocomplementation and provide some corresponding characterizations. We show that relatively pseudocomplemented posets satisfying a certain simple identity in two variables are join-semilattices. Finally, we show that every relatively pseudocomplemented poset is distributive and that the converse holds for posets satisfying the ascending chain condition and one more natural condition. Suitable examples are provided.
LA - eng
KW - relatively pseudocomplemented poset; join-semilattice; distributive poset
UR - http://eudml.org/doc/294284
ER -

References

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  9. Crulis, J., Implication in sectionally pseudocomplemented posets, Acta Sci. Math. 74 (2008), 477-491. (2008) Zbl1199.03059MR2487926
  10. Köhler, P., 10.2307/1998339, Trans. AMS 268 (1981), 103-126. (1981) Zbl0473.06003MR0628448DOI10.2307/1998339
  11. Larmerová, J., Rachůnek, J., Translations of distributive and modular ordered sets, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 27 (1988), 13-23. (1988) Zbl0693.06003MR1039879
  12. Nemitz, W. C., 10.2307/1994200, Trans. AMS 117 (1965), 128-142. (1965) Zbl0674.06003MR0176944DOI10.2307/1994200
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