Displaying similar documents to “On idempotent modifications of 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.

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...

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.

Normalization of M V -algebras

Ivan Chajda, Radomír Halaš, Jan Kühr, Alena Vanžurová (2005)

Mathematica Bohemica

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We consider algebras determined by all normal identities of M V -algebras, i.e. algebras of many-valued logics. For such algebras, we present a representation based on a normalization of a sectionally involutioned lattice, i.e. a q -lattice, and another one based on a normalization of a lattice-ordered group.