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Selected Properties of Some Generalizations of BCK Algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 89-103

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The notion of a RM algebra, introduced recently, is a generalization of many other algebras of logic. The class of RM algebras contains (weak-)BCC algebras, BCH algebras, BCI algebras, BCK algebras and many others. A RM algebra is an algebra A = (A; →, 1) of type (2, 0) satisfying the identities: x → x = 1 and 1 → x = x. In this paper we study the set of maximal elements of a RM algebra, branches of a RM algebra and moreover translation deductive systems of a RM algebra giving so called the Representation Theorem for RM algebras.
Keywords: RM algebra, deductive system 
Dymek, Grzegorz. Selected Properties of Some Generalizations of BCK Algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 89-103. http://geodesic.mathdoc.fr/item/DMGAA_2020_40_1_a7/
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