It is shown that unification in primal algebras is unitary, i.e. if an equation has a solution, it has a single most general one. Two unification algorithms, based on equation solving techniques for Boolean algebras due to Boole and Löwenheim, are studied in detail. Applications include certain finite Post algebras and matrix rings over finite fields. The former are algebraic models for many-valued logics, the latter cover in particular modular arithmetic.
Then unification is extended from primal algebras to their direct powers which leads to unitary unification algorithms covering finite Post algebras, finite, semisimple Artinian rings, and finite, semisimple non-abelian groups.
Finally we use the fact that the variety generated by a primal algebra coincides with the class of its subdirect powers. This yields unitary unification algorithms for the equational theories of Post algebras and p-rings.