Displaying similar documents to “Direct product decompositions of bounded commutative residuated ℓ -monoids”

Banaschewski’s theorem for generalized M V -algebras

Ján Jakubík (2007)

Czechoslovak Mathematical Journal

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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.

On central atoms of Archimedean atomic lattice effect algebras

Martin Kalina (2010)

Kybernetika

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If element z of a lattice effect algebra ( E , ⊕ , 0 , 1 ) is central, then the interval [ 0 , z ] is a lattice effect algebra with the new top element z and with inherited partial binary operation ⊕ . It is a known fact that if the set C ( E ) of central elements of E is an atomic Boolean algebra and the supremum of all atoms of C ( E ) in E equals to the top element of E , then E is isomorphic to a direct product of irreducible effect algebras ([16]). In [10] Paseka and Riečanová published as open problem whether C ( E ) is...

Epimorphisms between finite MV-algebras

Aldo V. Figallo, Marina B. Lattanzi (2017)

Mathematica Bohemica

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MV-algebras were introduced by Chang to prove the completeness of the infinite-valued Łukasiewicz propositional calculus. Recently, algebraic theory of MV-algebras has been intensively studied. Wajsberg algebras are just a reformulation of Chang MV-algebras where implication is used instead of disjunction. Using these equivalence, in this paper we provide conditions for the existence of an epimorphism between two finite MV-algebras A and B . Specifically, we define the mv-functions with...

State-homomorphisms on M V -algebras

Ján Jakubík (2001)

Czechoslovak Mathematical Journal

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Riečan [12] and Chovanec [1] investigated states in M V -algebras. Earlier, Riečan [11] had dealt with analogous ideas in D -posets. In the monograph of Riečan and Neubrunn [13] (Chapter 9) the notion of state is applied in the theory of probability on M V -algebras. We remark that a different definition of a state in an M V -algebra has been applied by Mundici [9], [10] (namely, the condition (iii) from Definition 1.1 above was not included in his definition of a state; in other words, only finite...