Baer Criterion for Injectivity of Projection Algebras

Projection algebras are M-sets for the monoid M = (ℕ^∞, min) which are used by computer scientists for algebraic specification of process algebras. In contrast to the case of modules it is well known that the Baer Criterion does not generally hold for injectivity of M-sets for an arbitrary monoid M. Here, introducing a closure operator, we prove that the Baer Criterion does hold for injectivity of projection algebras.