Equivalential algebras with conjunction on the regular elements
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 20 (2021), pp. 63-75.

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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.
Keywords: Fregean varieties, equivalential algebras, free algebras, free spectra
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Przybyło, Sławomir. Equivalential algebras with conjunction on the regular elements. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 20 (2021), pp. 63-75. http://geodesic.mathdoc.fr/item/AUPCM_2021_20_a4/

[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.