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Linear identities in graph algebras

Agata Pilitowska (2009)

Commentationes Mathematicae Universitatis Carolinae

We find the basis of all linear identities which are true in the variety of entropic graph algebras. We apply it to describe the lattice of all subvarieties of power entropic graph algebras.

Local versions of some congruence properties in single algebras

Ivan Chajda, Gerhard Dorfer, Helmut Länger (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We investigate some local versions of congruence permutability, regularity, uniformity and modularity. The results are applied to several examples including implication algebras, orthomodular lattices and relative pseudocomplemented lattices.

Locally finite M-solid varieties of semigroups

Klaus Denecke, Bundit Pibaljommee (2003)

Discussiones Mathematicae - General Algebra and Applications

An algebra of type τ is said to be locally finite if all its finitely generated subalgebras are finite. A class K of algebras of type τ is called locally finite if all its elements are locally finite. It is well-known (see [2]) that a variety of algebras of the same type τ is locally finite iff all its finitely generated free algebras are finite. A variety V is finitely based if it admits a finite basis of identities, i.e. if there is a finite set σ of identities such that V = ModΣ, the class of...

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