On class of atomic and coatomic modules

Fundemental properties of coatomic modules and its relations with some moduleclasses has been worked. This work consists of five chapters. All rings have anidentity and all modules are unitary right modules. The first chapter is a preparatorysection contains notions that will be needed. In the second chapter general propertiesof coatomic modules are given. Let Rad(M) is small module in M. Then M is acoatomic module if it satisfies one of the following condition:1) M=Rad(M) is semisimple.2) M is a weakly supplemented.3) M is linearly compakt.In the third chapter, coatomic modules in Dedekind domains and their properties arestudied. If R is a Dedekind domain, then the following statements are equivalent fora module MR:1) M is coatomic.2) Every submodule N of M is coatomic.3) For every submodule L of M, M=L is reduced.In the fourth chapter, d-coatomic modules and their properties are given. In addition,it is proved that M =Mni=1Mi is d-coatomic if only if each Mi (i = 1;2; :::;n) isd-coatomic. In the fifth chapter, properties of finitely coatomic modules and theirrelations with some other modules are given. In the sixth chapter, properties ofatomic modules and their relations with coatomic modules are given.