Subdirectly irreducible sectionally pseudocomplemented semilattices

Radomír Halaš; Jan Kühr

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 2, page 725-735
  • ISSN: 0011-4642

Abstract

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Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented semilattices.

How to cite

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Halaš, Radomír, and Kühr, Jan. "Subdirectly irreducible sectionally pseudocomplemented semilattices." Czechoslovak Mathematical Journal 57.2 (2007): 725-735. <http://eudml.org/doc/31158>.

@article{Halaš2007,
abstract = {Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented semilattices.},
author = {Halaš, Radomír, Kühr, Jan},
journal = {Czechoslovak Mathematical Journal},
keywords = {sectionally pseudocomplemented semilattice; weakly standard element; sectionally pseudocomplemented semilattice; weakly standard element},
language = {eng},
number = {2},
pages = {725-735},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Subdirectly irreducible sectionally pseudocomplemented semilattices},
url = {http://eudml.org/doc/31158},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Halaš, Radomír
AU - Kühr, Jan
TI - Subdirectly irreducible sectionally pseudocomplemented semilattices
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 2
SP - 725
EP - 735
AB - Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented semilattices.
LA - eng
KW - sectionally pseudocomplemented semilattice; weakly standard element; sectionally pseudocomplemented semilattice; weakly standard element
UR - http://eudml.org/doc/31158
ER -

References

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  2. An extension of relative pseudocomplementation to non-distributive lattices, Acta Sci. Math. (Szeged) 69 (2003), 491–496. (2003) Zbl1048.06005MR2034188
  3. Congruence Classes in Universal Algebra, Heldermann Verlag, Lemgo, 2003. (2003) MR1985832
  4. Sectionally pseudocomplemented lattices and semilattices. In: K. P. Shum (ed.) et al., Advances in Algebra. Proceedings of the ICM sattelite conference in algebra and related topics, Hong Kong, China, August 14–17, 2002. World Scientific, River Edge, 2003, pp. 282–290. (2003) MR2088449
  5. On varieties defined by pseudocomplemented nondistributive lattices, Publ. Math. Debrecen 63 (2003), 737–750. (2003) MR2020784
  6. General Lattice Theory (2nd edition), Birkhäuser Verlag, Basel-Boston-Berlin, 1998. (1998) MR1670580
  7. 10.1090/S0002-9947-1981-0628448-3, Trans. Amer. Math. Soc. 268 (1981), 103–126. (1981) MR0628448DOI10.1090/S0002-9947-1981-0628448-3
  8. 10.1090/S0002-9947-1965-0176944-9, Trans. Amer. Math. Soc. 117 (1965), 128–142. (1965) Zbl0128.24804MR0176944DOI10.1090/S0002-9947-1965-0176944-9
  9. A generalization of the notion of pseudo-complementedeness, Bull. Soc. Roy. Liège 37 (1968), 149–158. (1968) MR0228390

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