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Banaschewski’s theorem for generalized M V -algebras

Ján Jakubík (2007)

Czechoslovak Mathematical Journal

A generalized M V -algebra 𝒜 is called representable if it is a subdirect product of linearly ordered generalized M V -algebras. Let S be the system of all congruence relations ρ on 𝒜 such that the quotient algebra 𝒜 / ρ is representable. In the present paper we prove that the system S has a least element.

Basic pseudorings

Ivan Chajda, Miroslav Kolařík (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The concept of a basic pseudoring is introduced. It is shown that every orthomodular lattice can be converted into a basic pseudoring by using of the term operation called Sasaki projection. It is given a mutual relationship between basic algebras and basic pseudorings. There are characterized basic pseudorings which can be converted into othomodular lattices.

bi-BL-algebra

Mahdeieh Abbasloo, Arsham Borumand Saeid (2011)

Discussiones Mathematicae - General Algebra and Applications

In this paper, we introduce the notion of a bi-BL-algebra, bi-filter, bi-deductive system and bi-Boolean elements of a bi-BL-algebra and deal with bi-filters in bi-BL-algebra. We study this structure and construct the quotient of bi-BL-algebra. Also present a classification for examples of proper bi-BL-algebras.

Biframe compactifications

Anneliese Schauerte (1993)

Commentationes Mathematicae Universitatis Carolinae

Compactifications of biframes are defined, and characterized internally by means of strong inclusions. The existing description of the compact, zero-dimensional coreflection of a biframe is used to characterize all zero-dimensional compactifications, and a criterion identifying them by their strong inclusions is given. In contrast to the above, two sufficient conditions and several examples show that the existence of smallest biframe compactifications differs significantly from the corresponding...

Bipartite pseudo MV-algebras

Grzegorz Dymek (2006)

Discussiones Mathematicae - General Algebra and Applications

A bipartite pseudo MV-algebra A is a pseudo MV-algebra such that A = M ∪ M ̃ for some proper ideal M of A. This class of pseudo MV-algebras, denoted BP, is investigated. The class of pseudo MV-algebras A such that A = M ∪ M ̃ for all maximal ideals M of A, denoted BP₀, is also studied and characterized.

BL-algebras of basic fuzzy logic.

Esko Turunen (1999)

Mathware and Soft Computing

BL-algebras [Hajek] rise as Lindenbaum algebras from certain logical axioms familiar in fuzzy logic framework. BL-algebras are studied by means of deductive systems and co-annihilators. Duals of many theorems known to hold in MV-algebra theory remain valid for BL-algebras, too.

Boolean graphs

Juhani Nieminen (1988)

Commentationes Mathematicae Universitatis Carolinae

Bounded lattices with antitone involutions and properties of MV-algebras

Ivan Chajda, Peter Emanovský (2004)

Discussiones Mathematicae - General Algebra and Applications

We introduce a bounded lattice L = (L;∧,∨,0,1), where for each p ∈ L there exists an antitone involution on the interval [p,1]. We show that there exists a binary operation · on L such that L is term equivalent to an algebra A(L) = (L;·,0) (the assigned algebra to L) and we characterize A(L) by simple axioms similar to that of Abbott's implication algebra. We define new operations ⊕ and ¬ on A(L) which satisfy some of the axioms of MV-algebra. Finally we show what properties must be satisfied by...

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