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- W2554568276 abstract "In this article we are examining extensions and some basic diagrammatic properties of modules, in both cases from a new, point of view. As natural background for investigating the kind of problems we are dealing with, the virtual category of a module M is introduced, having as objects the submodules of M's subquotients modulo some identifications. In the case of extensions our approach implies viewing proportionality of extensions of (dually, by) a simple module by (resp. of) another simple as quotients of a certain quotient (which is in fact a subdirect product) of a projective cover, that comprises all those classes - or dually as submodules of a comprising submodule (which is a push-out) of an injective hull. In particular we become thus able to upgrade the Yoneda correspondence to a bimodule isomorphism. Basic steps toward the foundation of and investigation into the theory of Virtual Diagrams are also made here. In particular, the virtuality group A(D) of a virtual diagram D of a module M is introduced, generated by the D-visible virtual constituents of M, with respect to an addition that generalizes the one of submodules in a module." @default.
- W2554568276 created "2016-11-30" @default.
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- W2554568276 date "2016-09-26" @default.
- W2554568276 modified "2023-09-24" @default.
- W2554568276 title "From subdirect products to virtual diagrams & extensions" @default.
- W2554568276 hasPublicationYear "2016" @default.
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