Displaying similar documents to “State-homomorphisms on M V -algebras”

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 idempotent modifications of M V -algebras

Ján Jakubík (2007)

Czechoslovak Mathematical Journal

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The notion of idempotent modification of an algebra was introduced by Ježek. He proved that the idempotent modification of a group is subdirectly irreducible. For an M V -algebra 𝒜 we denote by 𝒜 ' , A and ℓ ( 𝒜 ) the idempotent modification, the underlying set or the underlying lattice of 𝒜 , respectively. In the present paper we prove that if 𝒜 is semisimple and ℓ ( 𝒜 ) is a chain, then 𝒜 ' is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras.

On intervals and isometries of M V -algebras

Ján Jakubík (2002)

Czechoslovak Mathematical Journal

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Let Int 𝒜 be the lattice of all intervals of an M V -algebra 𝒜 . In the present paper we investigate the relations between direct product decompositions of 𝒜 and (i) the lattice Int 𝒜 , or (ii) 2-periodic isometries on 𝒜 , respectively.

On product M V -algebras

Ján Jakubík (2002)

Czechoslovak Mathematical Journal

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In this paper we apply the notion of the product M V -algebra in accordance with the definition given by B. Riečan. We investigate the convex embeddability of an M V -algebra into a product M V -algebra. We found sufficient conditions under which any two direct product decompositions of a product M V -algebra have isomorphic refinements.