On locally finite varieties with undecidable equational theory. (Q1771892)

A variety \(\mathcal V\) is pseudorecursive if every finitely generated \(\mathcal V\)-free algebra has a decidable word problem but the equational theory of \(\mathcal V\) is undecidable. It is known that undecidability of the equational theory implies the undecidability of the uniform word problem. It is easy to establish the existence of many pseudorecursive varieties, even varieties of groups. However, all explicitly described examples in the literature are either nonassociative groupoids or varieties of groupoids with additional operations. The author combines a known method with some existing results to construct comparatively basic pseudorecursive varieties of semigroups and of groups. A large class of examples is described.