Displaying similar documents to “Two enumeration principles for free algebras”

A Characterization of Varieties of Associative Algebras of Exponent two

Giambruno, A., Zaicev, M. (2000)

Serdica Mathematical Journal

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∗The first author was partially supported by MURST of Italy; the second author was par- tially supported by RFFI grant 99-01-00233. It was recently proved that any variety of associative algebras over a field of characteristic zero has an integral exponential growth. It is known that a variety V has polynomial growth if and only if V does not contain the Grassmann algebra and the algebra of 2 × 2 upper triangular matrices. It follows that any variety with overpolynomial growth...

A scoop from groups: equational foundations for loops

Phillips, J. D., Petr Vojtěchovský (2008)

Commentationes Mathematicae Universitatis Carolinae

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Groups are usually axiomatized as algebras with an associative binary operation, a two-sided neutral element, and with two-sided inverses. We show in this note that the same simplicity of axioms can be achieved for some of the most important varieties of loops. In particular, we investigate loops of Bol-Moufang type in the underlying variety of magmas with two-sided inverses, and obtain ``group-like'' equational bases for Moufang, Bol and C-loops. We also discuss the case when the inverses...