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Topological representation for monadic implication algebras

100%
Abad M., Cimadamore C., Díaz Varela J.
Open Mathematics
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2009
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tom 7
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nr 2
299-309
EN
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 implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.
2
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A Hadamard product involving inverse-positive matrices

100%
Gassó M. T., Torregrosa J. R., Abad M.
Special Matrices
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2015
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tom 3
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nr 1
EN
In this paperwe study the Hadamard product of inverse-positive matrices.We observe that this class of matrices is not closed under the Hadamard product, but we show that for a particular sign pattern of the inverse-positive matrices A and B, the Hadamard product A ◦ B−1 is again an inverse-positive matrix.
3
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An equivalence between varieties of cyclic Post algebras and varieties generated by a finite field

88%
Abad M., Díaz Varela J., López Martinolich B., C. Vannicola M., Zander M.
Open Mathematics
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2006
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tom 4
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nr 4
547-561
EN
In this paper we give a term equivalence between the simple k-cyclic Post algebra of order p, L p,k, and the finite field F(p k) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain an interpretation Φ1 of the variety V(L p,k) generated by L p,k into the variety V(F(p k)) generated by F(p k) and an interpretation Φ2 of V(F(p k)) into V(L p,k) such that Φ2Φ1(B) = B for every B ε V(L p,k) and Φ1Φ2(R) = R for every R ε V(F(p k)).
4
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Closure Łukasiewicz algebras

88%
Abad M., Cimadamore C., Díaz Varela J., Rueda L., Suardíaz A.
Open Mathematics
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2005
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tom 3
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nr 2
215-227
EN
In this paper, the variety of closure n-valued Łukasiewicz algebras, that is, Łukasiewicz algebras of order n endowed with a closure operator, is investigated. The lattice of subvarieties in the particular case in which the open elements form a three-valued Heyting algebra is obtained.
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