Characterizations of 0-distributive posets

Vinayak V. Joshi; B. N. Waphare

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 1, page 73-80
  • ISSN: 0862-7959

Abstract

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The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

How to cite

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Joshi, Vinayak V., and Waphare, B. N.. "Characterizations of 0-distributive posets." Mathematica Bohemica 130.1 (2005): 73-80. <http://eudml.org/doc/249581>.

@article{Joshi2005,
abstract = {The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.},
author = {Joshi, Vinayak V., Waphare, B. N.},
journal = {Mathematica Bohemica},
keywords = {0-distributive; pseudocomplement; sectionally semi-complemented poset; ideal lattice; pseudocomplement; sectionally semi-complemented poset; ideal lattice},
language = {eng},
number = {1},
pages = {73-80},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterizations of 0-distributive posets},
url = {http://eudml.org/doc/249581},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Joshi, Vinayak V.
AU - Waphare, B. N.
TI - Characterizations of 0-distributive posets
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 1
SP - 73
EP - 80
AB - The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.
LA - eng
KW - 0-distributive; pseudocomplement; sectionally semi-complemented poset; ideal lattice; pseudocomplement; sectionally semi-complemented poset; ideal lattice
UR - http://eudml.org/doc/249581
ER -

References

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  10. 10.4153/CMB-1978-080-6, Canad. Math. Bull. 21 (1978), 469–475. (1978) MR0523589DOI10.4153/CMB-1978-080-6
  11. A generalization of the notion of pseudo-complementedness, Bull. Soc. Roy. Sci. Liège 37 (1968), 149–158. (1968) Zbl0162.03501MR0228390
  12. Distributive semilattices and Boolean lattices, Bull. Soc. Roy. Sci. Liège 41 (1972), 5–10. (1972) Zbl0237.06011MR0307991
  13. 10.1090/S0002-9939-1971-0272687-X, Proc. Amer. Math. Soc. 28 (1971), 9–17. (1971) Zbl0218.06002MR0272687DOI10.1090/S0002-9939-1971-0272687-X

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