Modules that can be characterized by the lifting of homomorphisms from closed submodules to the module itself.
by
Catarina Santa-Clara
Universidade de Lisboa, Portugal
Coauthors: Patrick F. Smith

A module M is quasi-injective if, for any submodule N of M, any homomorphism \alpha: N --> M can be lifted to a homomorphism \beta: M --> M. Continuous and quasi-continuous modules are other classes of modules that can be characterized by the lifting of homomorphisms from certain submodules to the module itself, as was shown by P. F. Smith, and A. Tercan (Continuous and quasi-continuous modules, Houston J. Math. 18 (1992), 339-348).

We are concerned with the study of self-c-injective modules, i.e., modules that can be characterized by the lifting of homomorphisms from closed submodules to the module itself. Extending modules are an example of modules with this property.

Date received: February 15, 1999