Deductive systems of pseudo-M algebras

Deductive systems of pseudo-M algebras

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The class of pseudo-M algebras contains pseudo-BCK, pseudo-BCI, pseudo-BCH, pseudo-BE, sheepshead bay boats 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 cubs foam finger 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.