Invertibility of Multiplication Modules
نویسنده
چکیده
Invertibility of multiplication modules All rings are commutative with 1 and all modules are unital. Let R be a ring and M an R-module. M is called multiplication if for each submodule N of M, N=IM for some ideal I of R. Multiplication modules have recently received considerable attention during the last twenty years. In this talk we give the de nition of invertible submodules as a natural generalization of invertible ideals, then we introduce the concept of Dedekind modules and Prufer modules. An R-module M is Dedekind ( resp. Prufer) if every non-zero ( resp. nonzero nitely generated) submodule of M is invertible. We introduce and investigate the concepts of generalized multiplication Dedekind modules and almost multiplication Dedekind modules. We also give some properties of non nitely generated submodules of faithful multiplication valuation modules and nally we characterize faithful multiplication modules via m-canonical submodules.
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