Abstract
In this paper, we study S-Principal ideal multiplication modules. Let be a commutative ring with a multiplicatively closed set and an A-module. A submodule N of M is said to be an S-multiple of M if there exist and a principal ideal I of A such that . is said to be an S-principal ideal multiplication module if every submodule of is an S-multiple of M. Various examples and properties of S-principal ideal multiplication modules are given. We investigate the conditions under which the trivial extension is an -principal ideal ring. Also, we prove Cohen type theorem for S-principal ideal multiplication modules in terms of S-prime submodules.
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