Dual Goldie and EC-complement Versions of the Extending Property

Abstract

It is well known that lifting modules are dual to extending modules, and there are plentiful of works on this subject. In this chapter, we consider modules with a property that is dual to Goldie extending property. Such modules are called Goldie*- supplemented modules. We investigate this new class of modules and the class of H-supplemented modules. Using another equivalence relation which is based on the radical of a module, we introduce the classes of Goldie-rad-supplemented and rad-H-supplemented modules. Finally, we discuss extending and C ₁₁ properties on ec-complement submodules and obtain fundamental properties of these classes of modules.