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Foulis-Holland theorem for implicative-orthomodular lattices
Lavinia Corina Ciungu
We introduce the notion of distributivity for implicative-orthomodular lattices, proving an analogue result of the Foulis-Holland theorem. Based on this result, we characterize the…
Generalizations of quantum-Wajsberg algebras
Lavinia Corina Ciungu
Starting from involutive BE algebras, we redefine the pre-MV and meta-MV algebras, by introducing the notion of pre-Wajsberg and meta-Wajsberg algebras, as generalizations of quant…
Centers of quantum-Wajsberg algebras
Lavinia Corina Ciungu
We define the Wajsberg-center and the OML-center of a quantum-Wajsberg algebra, and study their structures. We prove that the Wajsberg-center is a Wajsberg subalgebra of a quantum-…
Implicative-orthomodular algebras
Lavinia Corina Ciungu
Starting from involutive BE algebras, we redefine the orthomodular algebras, by introducing the notion of implicative-orthomodular algebras. We investigate properties of implicativ…
Quantum B-algebras with involutions
Lavinia Corina Ciungu
The aim of this paper is to define and study the involutive and weakly involutive quantum B-algebras. We prove that any weakly involutive quantum B-algebra is a quantum B-algebra w…
Monadic pseudo BE-algebras
Lavinia Corina Ciungu
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…