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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...

Matrix identities involving multiplication and transposition

Karl Auinger, Igor Dolinka, Michael V. Volkov (2012)

Journal of the European Mathematical Society

We study matrix identities involving multiplication and unary operations such as transposition or Moore–Penrose inversion. We prove that in many cases such identities admit no finite basis.

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