Abstract

A modlle is called extending if every submodule is essential in a direct summand. More generally, the extending property can be restricted to certain classes of submodules, e.g. uniform submodules,emisimple submodules. Inthis paper, we consider the extending property for the class of (essentially) finitely generated submodules. We study properties of this type of modules, decompositions and the relationship to finitely presented modules.