State BCK-algebras and State-Morphism BCK-algebras
Commutative Algebra
2013-04-26 v1 Rings and Algebras
Abstract
In the paper, we define the notion of a state BCK-algebra and a state-morphism BCK-algebra extending the language of BCK-algebras by adding a unary operator which models probabilistic reasoning. We present a relation between state operators and state-morphism operators and measures and states on BCK-algebras, respectively. We study subdirectly irreducible state (morphism) BCK-algebras. We introduce the concept of an adjoint pair in BCK-algebras and show that there is a one-to-one correspondence between adjoint pairs and state-morphism operators. In addition, we show the generators of quasivarieties of state-morphism BCK-algebras.
Keywords
Cite
@article{arxiv.1304.6963,
title = {State BCK-algebras and State-Morphism BCK-algebras},
author = {R. A. Borzooei and A. Dvurečenskij and O. Zahiri},
journal= {arXiv preprint arXiv:1304.6963},
year = {2013}
}