Monadic pseudo BE-algebras

Year, pages: 2020, 1013 - 1040

In this paper we define the monadic pseudo BE-algebras and investigate their properties. We prove that the existential and universal quantifiers of a monadic pseudo BE-algebra form a residuated pair. Special properties are studied for the particular case of monadic bounded commutative pseudo BE-algebras. Monadic classes of pseudo BE-algebras are investigated and it is proved that the quantifiers on bounded commutative pseudo BE-algebras are also quantifiers on the corresponding pseudo MV-algebras. The monadic deductive systems and monadic congruences of monadic pseudo BE-algebras are defined and their properties are studied. It is proved that, in the case of a monadic distributive commutative pseudo BE-algebra there is a one-to-one correspondence between monadic congruences and monadic deductive systems, and the monadic quotient pseudo BE-algebra algebra is also defined.

Ciungu, L. 2020. Monadic pseudo BE-algebras. In Mathematica Slovaca, vol. 70, no.5, pp. 1013-1040. 0139-9918. DOI: https://doi.org/0.1515/ms-2017-0411

Ciungu, L. (2020). Monadic pseudo BE-algebras. Mathematica Slovaca, 70(5), 1013-1040. 0139-9918. DOI: https://doi.org/0.1515/ms-2017-0411

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava