Displaying similar documents to “On a theorem of Cantor-Bernstein type for algebras”

An algebraic version of the Cantor-Bernstein-Schröder theorem

Hector Freytes (2004)

Czechoslovak Mathematical Journal

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The Cantor-Bernstein-Schröder theorem of the set theory was generalized by Sikorski and Tarski to σ -complete boolean algebras, and recently by several authors to other algebraic structures. In this paper we expose an abstract version which is applicable to algebras with an underlying lattice structure and such that the central elements of this lattice determine a direct decomposition of the algebra. Necessary and sufficient conditions for the validity of the Cantor-Bernstein-Schröder...

Direct summands and retract mappings of generalized M V -algebras

Ján Jakubík (2008)

Czechoslovak Mathematical Journal

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In the present paper we deal with generalized M V -algebras ( G M V -algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, G M V -algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract mappings of G M V -algebras. The relations between G M V -algebras and lattice ordered groups are essential for this investigation.

Isometries of generalized M V -algebras

Ján Jakubík (2007)

Czechoslovak Mathematical Journal

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In this paper we investigate the relations between isometries and direct product decompositions of generalized M V -algebras.

Cantor-Bernstein theorem for lattices

Ján Jakubík (2002)

Mathematica Bohemica

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This paper is a continuation of a previous author’s article; the result is now extended to the case when the lattice under consideration need not have the least element.