Deductive systems of pseudo-M algebras

Authors

  • Andrzej Walendziak University of Natural Sciences and Humanities in Siedlce, Faculty of Exact and Natural Sciences, Siedlce

Keywords:

pseudo-M, pseudo-CI, pseudo-BCH, pseudo-BCK algebra, (translation) deductive system, congruence, quotient algebra

Abstract

The class of pseudo-M algebras contains pseudo-BCK, pseudo-BCI, pseudo-BCH, pseudo-BE, pseudo-CI algebras and many other algebras of logic. In this paper, the notion of deductive system in a pseudo-M algebra is introduced and its elementary properties are investigated. Closed deductive systems are defined and studied. The homomorphic properties of (closed) deductive systems are provided. The concepts of translation deductive systems and R-congruences in pseudo-M algebras are introduced and investigated. It is shown that there is a bijection between closed translation deductive systems and R-congruences. Finally, the construction of quotient algebra A/D of a pseudo-M algebra A via a translation deductive system D of A is given.

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Published

2022-12-19

How to Cite

Walendziak, A. (2022). Deductive systems of pseudo-M algebras. Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 21, 93–116. Retrieved from https://studmath.uken.krakow.pl/article/view/9650

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Vol. 21 (2022)

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