Approaches to a problem of constructing free algebras and examples of free groupoids
by
Lidija Goracinova Ilieva
Pedagogical Faculty "Gotse Delchev",Macedonia
Coauthors: Smile Markovski

The difficulties of obtaining a description of the free algebras in a variety given by a set of defining identities depends on the complexity of the interrelationships between the identities in the variety. Although there is no general method to resolve this problem in each particular case, some approaches turn out to be useful in the attempt to construct free algebras: direct approach by chosing a free algebra - model, description of the congruence generated by the identities, term reduction, replacement scheme, construction by a chain of partial algebras, and construction with a sequence of algebras. In that way were obtained descriptions of free groupoids in many varieties.

Date received: July 30, 2001