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An algorithm for free algebras. (English) Zbl 1224.08006

The author presents an algorithm for constructing the free algebra over a given partial algebra in the variety determined by a finite list of equations. This algorithm uses so-called reductive steps based on so-called renovations and extensive steps which extend the partial \(n\)-ary operation for a non-defined \(n\)-tuple (the so-called spark). The algorithm succeeds whenever the desired free algebra is finite, i.e. in particular, in locally finite and finitely presented varieties. A number of examples are included, and the algorithm has already been implemented as a computer program.

MSC:

08B20 Free algebras
08A55 Partial algebras
08B05 Equational logic, Mal’tsev conditions
08-04 Software, source code, etc. for problems pertaining to general algebraic systems
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