An algebraic version of the Cantor-Bernstein-Schröder theorem

Title:

An algebraic version of the Cantor-Bernstein-Schröder theorem

Creator:

Freytes, Hector

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:bd786251-8b53-4bee-bc78-338392bc408b
uuid:bd786251-8b53-4bee-bc78-338392bc408b

Subject:

lattices, central elements, factor congruences, and varieties

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The Cantor-Bernstein-Schröder theorem of the set theory was generalized by Sikorski and Tarski to $\sigma $-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 theorem for these algebras are given. These results are applied to obtain versions of the Cantor-Bernstein-Schröder theorem for $\sigma $-complete orthomodular lattices, Stone algebras, $BL$-algebras, $MV$-algebras, pseudo $MV$-algebras, Łukasiewicz and Post algebras of order $n$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

609-621

Source:

Czechoslovak Mathematical Journal | 2004 Volume:54 | Number:3

Harvested from:

CDK

Metadata only:

false