Irreducible and Prime Deductive Systems of Some Generalizations of BCK Algebras
Some generalizations of BCK algebras (such as, from example, RM, BH, pre-BBBCC and pre-BCK algebras) are considered. It is proved that the set of all deductive systems of a pre-BBBCC algebra is an algebraic distributive lattice. Irreducible deductive systems and prime deductive systems of RM algebras are introduced and studied. In particular, the homomorphic properties of these deductive systems are provided. Finally, subdirect products of BH algebras by using prime deductive systems are investigated.
Keywords: RM, BH, BCI, BCK algebra, (irreducible, prime, maximal) deductive system, homomorphism, subdirect product
Mathematics Subject Classification (2010): 03G25, 06A06, 06F35