Locally Cyclic Projective Modules
نویسندگان
چکیده
Let R be a commutative ring with identity and M an R–module. If M is either locally cyclic projective or faithful multiplication then M is locally either zero or isomorphic to R. We investigate locally cyclic projective modules and the properties they have in common with faithful multiplication modules. Our main tool is the trace ideal. We see that the module structure of a locally cyclic projective module and its trace ideal are closely related. We prove cancellation laws involving projective modules and their trace ideals. Among various applications, we show that the product of a prime ideal and a locally cyclic projective module is a prime submodule.
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