Abstract
Let M be an R-module. If for every submodule N of M; there exists an element r 2 R such that N = rM; then we say that M is a principal ideal multiplication module. In this paper, the relations between principal ideal multiplication modules, multiplication modules, cyclic modules, and modules over principal ideal rings are studied. It is proved that every principal ideal multiplication module over any quotient of a Dedekind domain is cyclic. Also, every principal ideal multiplication module with prime annihilator ideal is cyclic.
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