Characterizations of the 0 -distributive semilattice

P. Balasubramani

Mathematica Bohemica (2003)

  • Volume: 128, Issue: 3, page 237-252
  • ISSN: 0862-7959

Abstract

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The 0 -distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for 0 -distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.

How to cite

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Balasubramani, P.. "Characterizations of the $0$-distributive semilattice." Mathematica Bohemica 128.3 (2003): 237-252. <http://eudml.org/doc/249237>.

@article{Balasubramani2003,
abstract = {The $0$-distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for $0$-distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.},
author = {Balasubramani, P.},
journal = {Mathematica Bohemica},
keywords = {semilattice; prime ideal; filter; semilattice; prime ideal; filter},
language = {eng},
number = {3},
pages = {237-252},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterizations of the $0$-distributive semilattice},
url = {http://eudml.org/doc/249237},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Balasubramani, P.
TI - Characterizations of the $0$-distributive semilattice
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 3
SP - 237
EP - 252
AB - The $0$-distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for $0$-distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.
LA - eng
KW - semilattice; prime ideal; filter; semilattice; prime ideal; filter
UR - http://eudml.org/doc/249237
ER -

References

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  1. Characterizations of the 0 -distributive lattice, J. Pure Appl. Math. 32 (2001), 315–324. (2001) MR1826759
  2. Lattice Theory First Concepts and Distributive Lattices, W. H. Freeman, San Francisco, 1971. (1971) MR0321817
  3. Prime α -ideals in a 0 -distributive lattice, J. Pure Appl. Math. 17 (1986), 331–337. (1986) Zbl0595.06010MR0835346
  4. 10.4153/CMB-1978-080-6, Canad. Math. Bull. 21 (1978), 469–475. (1978) MR0523589DOI10.4153/CMB-1978-080-6
  5. 10.1007/BF01847920, Period. Math. Hungar. 13 (1982), 237–246. (1982) MR0683850DOI10.1007/BF01847920
  6. Introduction to Lattice Theory, Academic Press, New York, 1963. (1963) MR0166118
  7. A generalization of the notion of pseudocomplementedness, Bull. Soc. Roy. Sci. Liege 37 (1968), 149–158. (1968) MR0228390
  8. Distributive semilattices and Boolean lattices, Bull. Soc. Roy. Liege 41 (1972), 5–10. (1972) Zbl0237.06011MR0307991
  9. 10.1090/S0002-9939-1971-0272687-X, Proc. Amer. Math. Soc. 28 (1971), 9–17. (1971) MR0272687DOI10.1090/S0002-9939-1971-0272687-X
  10. Semiideals in semilattices, Col. Math. 30 (1974), 203–212. (1974) 

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