On the number of generators of an algebra

Abstract A classical theorem of Forster asserts that a finite module M of rank ≤n over a Noetherian ring of Krull dimension d can be generated by n + d elements. We prove a generalization of this result, with “module” replaced by “algebra”. Here we allow arbitrary finite algebras, not necessarily unital, commutative or associative. Forster's theorem can be recovered as a special case by viewing a module as an algebra where the product of any two elements is 0.