Strongly (Comletely) Hollow Submodules I

Abstract

Let R be a commutative ring with unity and let M be an R-module. In this paper we study strongly (completely) hollow submodules and quasi-hollow submodules. We investigate the basic properties of these submodules and the relationships between them. Also we study the be behavior of these submodules under certain class of modules such as compultiplication, distributive, multiplication and scalar modules. In part II we shall continue the study of these submodules.

Keywords

• Strongly (completely)-hollow submodules, distributive modules, multiplication (comultiplication) modules, scalar modules.