A Note on Pseudo-Kleene Algebras

Ivan Chajda

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2016)

  • Volume: 55, Issue: 1, page 39-45
  • ISSN: 0231-9721

Abstract

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We introduce the concept of a pseudo-Kleene algebra which is a non-distributive modification of a Kleene algebra introduced by J. A. Kalman [Kalman, J. A.: Lattices with involution. Trans. Amer. Math. Soc. 87 (1958), 485–491.]. Basic properties of pseudo-Kleene algebras are studied. For pseudo-Kleene algebras with a fix-point there are determined subdirectly irreducible members.

How to cite

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Chajda, Ivan. "A Note on Pseudo-Kleene Algebras." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 55.1 (2016): 39-45. <http://eudml.org/doc/286702>.

@article{Chajda2016,
abstract = {We introduce the concept of a pseudo-Kleene algebra which is a non-distributive modification of a Kleene algebra introduced by J. A. Kalman [Kalman, J. A.: Lattices with involution. Trans. Amer. Math. Soc. 87 (1958), 485–491.]. Basic properties of pseudo-Kleene algebras are studied. For pseudo-Kleene algebras with a fix-point there are determined subdirectly irreducible members.},
author = {Chajda, Ivan},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Antitone involution; De Morgan laws; Kleene algebra; distributive lattice; pseudo-Kleene algebra; subdirectly irreducible},
language = {eng},
number = {1},
pages = {39-45},
publisher = {Palacký University Olomouc},
title = {A Note on Pseudo-Kleene Algebras},
url = {http://eudml.org/doc/286702},
volume = {55},
year = {2016},
}

TY - JOUR
AU - Chajda, Ivan
TI - A Note on Pseudo-Kleene Algebras
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2016
PB - Palacký University Olomouc
VL - 55
IS - 1
SP - 39
EP - 45
AB - We introduce the concept of a pseudo-Kleene algebra which is a non-distributive modification of a Kleene algebra introduced by J. A. Kalman [Kalman, J. A.: Lattices with involution. Trans. Amer. Math. Soc. 87 (1958), 485–491.]. Basic properties of pseudo-Kleene algebras are studied. For pseudo-Kleene algebras with a fix-point there are determined subdirectly irreducible members.
LA - eng
KW - Antitone involution; De Morgan laws; Kleene algebra; distributive lattice; pseudo-Kleene algebra; subdirectly irreducible
UR - http://eudml.org/doc/286702
ER -

References

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  1. Birkhoff, G., Lattice Theory, . Amer. Math. Soc. Colloqnium Publ. 25, second edition, American Mathematical Society, New York, 1948. (1948) Zbl0033.10103MR0029876
  2. Cignoli, R., 10.1090/S0002-9939-1975-0357259-4, . Proc. Amer. Math. Soc. 47 (1975), 269–278. (1975) Zbl0301.06009MR0357259DOI10.1090/S0002-9939-1975-0357259-4
  3. Crvenkovič, S., Madarasz, R. Sz., 10.1016/0304-3975(93)90228-L, . Theoret. Comput. Sci. 108 (1993), 17–24. (1993) Zbl0778.03006MR1203820DOI10.1016/0304-3975(93)90228-L
  4. Kalman, J. A., 10.1090/S0002-9947-1958-0095135-X, . Trans. Amer. Math. Soc. 87 (1958), 485–491. (1958) Zbl0228.06003MR0095135DOI10.1090/S0002-9947-1958-0095135-X

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