Equivalential algebras with conjunction on the regular elements

Sławomir Przybyło

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2021)

  • Volume: 20, page 63-75
  • ISSN: 2300-133X

Abstract

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We introduce the definition of the three-element equivalential algebra R with conjunction on the regular elements. We study the variety generated by R and prove the Representation Theorem. Then, we construct the finitely generated free algebras and compute the free spectra in this variety.

How to cite

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Sławomir Przybyło. "Equivalential algebras with conjunction on the regular elements." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 20 (2021): 63-75. <http://eudml.org/doc/296812>.

@article{SławomirPrzybyło2021,
abstract = {We introduce the definition of the three-element equivalential algebra R with conjunction on the regular elements. We study the variety generated by R and prove the Representation Theorem. Then, we construct the finitely generated free algebras and compute the free spectra in this variety.},
author = {Sławomir Przybyło},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {Fregean varieties; equivalential algebras; free algebras; free spectra},
language = {eng},
pages = {63-75},
title = {Equivalential algebras with conjunction on the regular elements},
url = {http://eudml.org/doc/296812},
volume = {20},
year = {2021},
}

TY - JOUR
AU - Sławomir Przybyło
TI - Equivalential algebras with conjunction on the regular elements
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2021
VL - 20
SP - 63
EP - 75
AB - We introduce the definition of the three-element equivalential algebra R with conjunction on the regular elements. We study the variety generated by R and prove the Representation Theorem. Then, we construct the finitely generated free algebras and compute the free spectra in this variety.
LA - eng
KW - Fregean varieties; equivalential algebras; free algebras; free spectra
UR - http://eudml.org/doc/296812
ER -

References

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  1. Burris, Stanley and Hanamantagouda P. Sankappanavar. A Course in Universal Algebra. Berlin: Springer, 2012. 
  2. Freese, Ralph and Ralph Mckenzie. Commutator theory for congruence modular varieties. Vol. 125 of London Math. Soc. Lecture Note Ser. Cambridge: Cambridge Univ. Press., 1987. 
  3. Hagemann J. "On regular and weakly regular congruences." Darmstadt: preprint no. 75, 1973. 
  4. Hobby, David, and Ralph McKenzie, The structure of finite algebras. Vol. 76 of Contemporary Mathematics. Providence: American Mathematical Society, 1988. 
  5. Idziak, Paweł M., and Katarzyna Słomczyńska. "Polynomially rich algebras." J. Pure Appl. Algebra 156, no. 1 (2001): 33-68. 
  6. Idziak, Paweł M., and Katarzyna Słomczyńska, and Andrzej Wronski. "Commutator in equivalential algebras and Fregean varieties." Algebra Universalis 65, no. 4 (2011): 331-340. 
  7. Idziak, Paweł M., and Katarzyna Słomczyńska, and Andrzej Wronski. "Fregean Varieties." Internat. J. Algebra Comput. 19, no. 5 (2009): 595-645. 
  8. Kabziński, Jacek K. and Andrzej Wroński. "On equivalential algebras." Proceedings of the 1975 International Symposium on Multipe-Valued Logic, 419-428. Bloomington: Indiana University, 1975. 
  9. McKenzie, Ralph, and George McNulty, and Walter Taylor. Algebras, Lattices, Varieties. Vol. 1. Monterey: Wadsworth and Brooks/Cole Advanced Books & Software, 1987. 
  10. Słomczyńska, Katarzyna. "Free spectra of linear equivalential algebras." J. Symbolic Logic 70, no. 4 (2005): 1341-1358. 

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