The Implicative Property for Some Generalizations of BCK Algebras
We consider various generalizations of BCK algebras (RML, aRML, *RML, aRML**, pre-BCC, pre-BCK, weak BCK* algebras and many others). We investigate the property of implicativity for these algebras. We prove that every implicative *RML** algebra is a pre-BCC algebra and also show that implicative *aRML** algebras are Tarski algebras. Moreover, we give several examples of implicative finite algebras. Finally, we review some classes of implicative RML algebras and prove that they are varieties.
Keywords: RM, RML, aRML, RML**, BCC, pre-BCK, BCK algebra, implicativity
Mathematics Subject Classification (2010): 03G25, 06A06, 06F35