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1
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Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients

100%
Piciu D.
Open Mathematics
|
2004
|
tom 2
|
nr 2
199-217
EN
The aim of this paper is to define the notions of pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (taking as a guide-line the elegant construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambek-see [14], p.36). For some informal explanations of the notion of fraction see [14], p. 37. In the last part of this paper the existence of the maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (Theorem 4.5) is proven and I give explicit descriptions of this MV-algebra for some classes of pseudo MV-algebras.
2
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An equivalence between varieties of cyclic Post algebras and varieties generated by a finite field

84%
Abad M., Díaz Varela J., López Martinolich B., C. Vannicola M., Zander M.
Open Mathematics
|
2006
|
tom 4
|
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)).
3
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Representation of Hilbert algebras and implicative semilattices

84%
Celani S.
Open Mathematics
|
2003
|
tom 1
|
nr 4
561-572
EN
In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.
4
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The prime and maximal spectra and the reticulation of BL-algebras

84%
Leuštean L.
Open Mathematics
|
2003
|
tom 1
|
nr 3
382-397
EN
In this paper we study the prime and maximal spectra of a BL-algebra, proving that the prime spectrum is a compact T 0 topological space and that the maximal spectrum is a compact Hausdorff topological space. We also define and study the reticulation of a BL-algebra.
5
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Congruences, ideals and annihilators in standard QBCC-algebras

84%
Halaš R., Plojhar L.
Open Mathematics
|
2005
|
tom 3
|
nr 1
83-97
EN
We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels.
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