LocalMV-algebras

Belluce, L. P.; Nola, Antonio Di; Lettieri, A.

doi:10.1007/bf02844626

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Weak Boolean Products Of Local Bl-algebras2

Introduction2

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Cited by 46 publications

(40 citation statements)

References 3 publications

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“…Local BL-algebras are studied in [21,22] in the same way as local MV-algebras are analyzed in [2]. Thus, a BL-algebra is called local iff it has a unique ultrafilter.…”

Section: Weak Boolean Products Of Local Bl-algebrasmentioning

confidence: 99%

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Boolean Products of BL-Algebras

Nola

Georgescu

Leuştean

2000

Journal of Mathematical Analysis and Applications

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“…Local BL-algebras are studied in [21,22] in the same way as local MV-algebras are analyzed in [2]. Thus, a BL-algebra is called local iff it has a unique ultrafilter.…”

Section: Weak Boolean Products Of Local Bl-algebrasmentioning

confidence: 99%

“…As in the case of MV-algebras (see [2,11]), a BL-algebra A is called perfect if it is local and for any a ∈ A, ord a < ∞ implies ord a − = ∞…”

Section: Weak Boolean Products Of Perfect Bl-algebrasmentioning

confidence: 99%

Boolean Products of BL-Algebras

Nola

Georgescu

Leuştean

2000

Journal of Mathematical Analysis and Applications

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“…Following [2], in [15] local pseudo-MV algebras were defined and some classes of local pseudo-MV algebras were studied. Thus, a pseudo-MV algebra is local if and only if it has a unique maximal ideal and a local pseudo-MV algebra is: …”

Section: Proposition 124 ([4 Corollary 234]) a Pseudo-bl Algebra mentioning

confidence: 99%

Some classes of pseudo-BL algebras

Georgescu

Leuştean

2002

J. Aust. Math. Soc.

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Pseudo-BL algebras are noncommutative generalizations of BL-algebras and they include pseudo-MV algebras, a class of structures that are categorically equivalent to /-groups with strong unit. In this paper we characterize directly indecomposable pseudo-BL algebras and we define and study different classes of these structures: local, good, perfect, peculiar, and (strongly) bipartite pseudo-BL algebras.

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“…Perfect MV-algebras, introduced by Belluce, Di Nola and Lettieri in [2], may be viewed as the most compelling examples of non-Archimedean MV-algebras, in such a sense that they are generated by their infinitesimals. In a perfect MV-algebra, every element belongs either to its radical or its coradical.…”

Section: Introduction and Basic Definitionsmentioning

confidence: 99%

Discrete (n + 1)-valued states and n-perfect pseudo-effect algebras

2013

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We give sufficient and necessary conditions to guarantee that a pseudo-effect algebra admits an (n + 1)-valued discrete state. We introduce n-perfect pseudoeffect algebras as algebras which can be split into n + 1 comparable slices. We prove that the category of strong n-perfect pseudo-effect algebras is categorically equivalent to the category of torsion-free directed partially ordered groups of a special type.

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LocalMV-algebras

Cited by 46 publications

References 3 publications

Boolean Products of BL-Algebras

Boolean Products of BL-Algebras

Some classes of pseudo-BL algebras

Discrete (n + 1)-valued states and n-perfect pseudo-effect algebras

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