Some types of implicative ideals

Ladislav Beran

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 2, page 219-225
  • ISSN: 0010-2628

Abstract

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This paper studies basic properties for five special types of implicative ideals (modular, pentagonal, even, rectangular and medial). The results are used to prove characterizations of modularity and distributivity.

How to cite

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Beran, Ladislav. "Some types of implicative ideals." Commentationes Mathematicae Universitatis Carolinae 39.2 (1998): 219-225. <http://eudml.org/doc/248271>.

@article{Beran1998,
abstract = {This paper studies basic properties for five special types of implicative ideals (modular, pentagonal, even, rectangular and medial). The results are used to prove characterizations of modularity and distributivity.},
author = {Beran, Ladislav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {implicative ideals; modular ideals; pentagonal ideals; even ideals; rectangular ideals; medial ideals; modularity; distributivity; implicative ideals; modular ideals; pentagonal ideals; even ideals; rectangular ideals; medial ideals; modularity; distributivity},
language = {eng},
number = {2},
pages = {219-225},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some types of implicative ideals},
url = {http://eudml.org/doc/248271},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Beran, Ladislav
TI - Some types of implicative ideals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 2
SP - 219
EP - 225
AB - This paper studies basic properties for five special types of implicative ideals (modular, pentagonal, even, rectangular and medial). The results are used to prove characterizations of modularity and distributivity.
LA - eng
KW - implicative ideals; modular ideals; pentagonal ideals; even ideals; rectangular ideals; medial ideals; modularity; distributivity; implicative ideals; modular ideals; pentagonal ideals; even ideals; rectangular ideals; medial ideals; modularity; distributivity
UR - http://eudml.org/doc/248271
ER -

References

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  1. Beran L., On semiprime ideals in lattices, Journ. Pure Appl. Algebra 64 (1990), 223-227. (1990) Zbl0703.06003MR1061299
  2. Beran L., Orthomodular Lattices (Algebraic Approach), Reidel Dordrecht (1985). (1985) Zbl0558.06008MR0784029
  3. Beran L., Salvati S., Boolean algebras revisited, Boll. Unione Matem. Italiana, ser. VII, 9 (sez. B) (1997), 895-901. Zbl0895.06007MR1491733
  4. Rav Y., Semiprime ideals in general lattices, Journ. Pure Appl. Algebra 56 (1989), 105-118. (1989) Zbl0665.06006MR0979666
  5. Salvati S., A characterization of Boolean algebras, Ricerche di Matematica 43 (1994), 357-363. (1994) Zbl0915.06005MR1324757
  6. Zassenhaus H., The Theory of Groups, (2nd ed.), Vandenhoeck & Ruprecht Göttingen (1958). (1958) Zbl0083.24517MR0091275

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