Translations, Endomorphisms, and Stable Equational Theories
Grzegorz Bancerek · 1996
Summary. Equational theories of an algebra, i.e. the equivalence relation closed under translations and endomorphisms, are formalized. The correspondence between equational theories and term rewriting systems is discussed in the paper. We get as the main result that any pair of elements of an algebra belongs to the equational theory generated by a set A of axioms iff the elements are convertible w.r.t. term rewriting reduction determined by A. The theory is developed according to [19].