Abstract
In this paper, we study the decompositions of an amply supplemented module M into a direct sum of cotype submodules. For this purpose, we introduce some conatural classes, such as the class of all q-molecular modules, the class of all q-bottomless modules, the class of all q-discrete modules and the class of all q-continuous modules, which are defined for every ring. We also find conditions on the structure of the cotype submodules of an amply supplemented module M, in order for M to have certain direct sum decompositions.
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