Characterization of Quasi-Coherent Modules that are Module Schemes |
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| Authors: | Amelia Álvarez Carlos Sancho Pedro Sancho |
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| Institution: | 1. Department of Mathematics , University of Extremadura , Badajoz, Spain aalarma@unex.es;3. Department of Mathematics , University of Salamanca , Salamanca, Spain;4. Department of Mathematics , University of Extremadura , Badajoz, Spain |
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| Abstract: | Let R be a commutative ring with unit, and let E be an R-module. We say the functor of R-modules E, defined by E(B) = E ? R B, is a quasi-coherent R-module, and its dual E* is an R-module scheme. Both types of R-module functors are essential for the development of the theory of the linear representations of an affine R-group. We prove that a quasi-coherent R-module E is an R-module scheme if and only if E is a projective R-module of finite type, and, as a consequence, we also characterize finitely generated projective R-modules. |
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| Keywords: | Module schemes Projective modules Quasi-coherent modules |
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