Ultra L I -ideals in lattice implication algebras

Ke Yun Qin; Yang Xu; Young Bae Jun

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 3, page 463-468
  • ISSN: 0011-4642

Abstract

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We define an ultra L I -ideal of a lattice implication algebra and give equivalent conditions for an L I -ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra L I -ideal.

How to cite

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Qin, Ke Yun, Xu, Yang, and Jun, Young Bae. "Ultra $LI$-ideals in lattice implication algebras." Czechoslovak Mathematical Journal 52.3 (2002): 463-468. <http://eudml.org/doc/30716>.

@article{Qin2002,
abstract = {We define an ultra $LI$-ideal of a lattice implication algebra and give equivalent conditions for an $LI$-ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra $LI$-ideal.},
author = {Qin, Ke Yun, Xu, Yang, Jun, Young Bae},
journal = {Czechoslovak Mathematical Journal},
keywords = {lattice implication algebra; (ultra) $LI$-ideal; finite additive property; lattice implication algebra; ultra LI-ideal; finite additivity property},
language = {eng},
number = {3},
pages = {463-468},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Ultra $LI$-ideals in lattice implication algebras},
url = {http://eudml.org/doc/30716},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Qin, Ke Yun
AU - Xu, Yang
AU - Jun, Young Bae
TI - Ultra $LI$-ideals in lattice implication algebras
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 3
SP - 463
EP - 468
AB - We define an ultra $LI$-ideal of a lattice implication algebra and give equivalent conditions for an $LI$-ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra $LI$-ideal.
LA - eng
KW - lattice implication algebra; (ultra) $LI$-ideal; finite additive property; lattice implication algebra; ultra LI-ideal; finite additivity property
UR - http://eudml.org/doc/30716
ER -

References

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  1. L I -ideals in lattice implication algebras, Bull. Korean Math. Soc. 35 (1998), 13–24. (1998) MR1609010
  2. Fuzzy L I -ideals in lattice implication algebras, J. Fuzzy Math. 7 (1999), 997–1003. (1999) MR1734015
  3. Positive implicative and associative filters of lattice implication algebras, Bull. Korean Math. Soc. 35(1) (1998), 53–61. (1998) MR1608994
  4. Homomorphisms in lattice implication algebras, Proc. of 5th Many-Valued Logical Congress of China (1992), 206–211. (1992) 
  5. Lattice implication algebras, J. Southwest Jiaotong University 1 (1993), 20–27. (1993) Zbl0966.03524
  6. On filters of lattice implication algebras, J. Fuzzy Math. 1 (1993), 251–260. (1993) MR1230317

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