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A reduction theorem for ring varieties whose subvariety lattice is distributive

Mikhail V. Volkov (2010)

Discussiones Mathematicae - General Algebra and Applications

We prove a theorem (for arbitrary ring varieties and, in a stronger form, for varieties of associative rings) which basically reduces the problem of a description of varieties with distributive subvariety lattice to the case of algebras over a finite prime field.

A survey of hereditary properties of graphs

Mieczysław Borowiecki, Izak Broere, Marietjie Frick, Peter Mihók, Gabriel Semanišin (1997)

Discussiones Mathematicae Graph Theory

In this paper we survey results and open problems on the structure of additive and hereditary properties of graphs. The important role of vertex partition problems, in particular the existence of uniquely partitionable graphs and reducible properties of graphs in this structure is emphasized. Many related topics, including questions on the complexity of related problems, are investigated.

An algebraic version of the Cantor-Bernstein-Schröder theorem

Hector Freytes (2004)

Czechoslovak Mathematical Journal

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 theorem for...

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