Abstract
In this paper, the notions of f-injective and f*-injective modules are indroduced. Elementary properties of these modules are given. For instance, a ring R is coherent iff any ultraproduct of f-injective modules is absolutaly pure. We prove that the class Sigma* of f*-injective modules is closed under ultraproducts. On the otherhand, Sigma* is not axiomatisable. For coherent rings R, Sigma* is axiomatisable iff every chi(0) -injective module is f*-injective. Further, it is shown that the class Sigma of f-injective modules is axiomatisable iff R is coherent and every chi(0)-injective module is f-injective. Finally, f-injective module H, such that every module embeds in an ultraprower of H, is given.