On injectivity of projection and separated projection algebras

Abstract

Projection spaces (algebras) were ¯rst introduced by Ehrig et. al. as an algebraic version of ultrametric spaces, and then studied by Giuli, Ebrahimi, Mahmoudi.  Computer scientists use projection algebras for algebraic specification of process algebras.  A kind of injectivity of separated projection algebras have been studied by Giuli.  In this paper, we extend this notion to all projection algebras, and introduce some other kind of injectivity, so called m and p-injectivity, and show, among other things, that injectivity, s-injectivity, and m-injectivity coincide, and so we get some more Baer criteria for injectivity.