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Zariski-type topology for implication algebras
(Wiley VCH Verlag, 2010-06)
In this work we provide a new topological representation for implication algebras in such a way that its one- point compactification is the topological space given in [1]. Some applications are given thereof.
Topological representation for monadic implication algebras
(De Gruyter, 2009-01-17)
In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic ...
Topological representation for implication algebras
(Birkhauser Verlag Ag, 2004-11)
In this paper we give a description of an implication algebra A as a union of a unique family of filters of a suitable Boolean algebra Bo(A), called the Boolean closure of A. From this representation we obtain a notion of ...
Representations of cubic lattices by symmetric implication algebras
(Springer, 2006-10-18)
In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries ...
Conditions for permutability of congruences in implication algebras
(Springer, 2009-09)
In this paper we give conditions on an implication algebra A so that two congruences θ1, θ2 on A permute, i.e. θ1 ○ θ2 = θ2 ○ θ1. We also provide simpler conditions for permutability in finite implication algebras. Finally ...
Free Łukasiewicz implication algebras
(Springer, 2008-06)
Łukasiewicz implication algebras are the {→,1}-subreducts of MV- algebras. They are the algebraic counterpart of Super-Łukasiewicz Implicational Logics investigated in Komori (Nogoya Math J 72:127-133, 1978). In this paper ...
On the free frontal implicative semilattice extension of a frontal Hilbert algebra
(Springer Verlag, 2019-11)
In this paper, we define a functor which is left adjoint to the forgetful functor from the category of frontal implicative semilattices to that of frontal Hilbert algebras.
Decomposability of free Łukasiewicz implication algebras
(Springer, 2006-11)
Łukasiewicz implication algebras are {→,1}-subreducts of Wajsberg algebras (MV-algebras). They are the algebraic counterpart of Super-Łukasiewicz Implicational logics investigated in Komori, Nogoya Math J 72:127-133, 1978. ...
Implicative subreducts of MV-algebras: free and weakly projective objects
(Birkhauser Verlag Ag, 2017-12)
In this article, we explore in some detail the free and weakly projective objects of the variety of Łukasiewicz implication algebras (the implicative subreducts of MV-algebras). We review the two already known descriptions ...
Symmetric implication zroupoids and identities of Bol–Moufang type
(Springer, 2018-07)
An algebra A= ⟨ A, → , 0 ⟩ , where → is binary and 0 is a constant, is called an implication zroupoid (I-zroupoid, for short) if A satisfies the identities: (I): (x→y)→z≈((z′→x)→(y→z)′)′, and (I0): 0 ′ ′≈ 0 , where x′: = ...