Uploaded October 2021 | Updated September 2026, 1 week ago

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This lecture is part of an online course on rings and modules.

We descibe some notions of duality for modules generalizing the dual of a vector space. We first discuss duality for free and projective modules, which is very siilar to the vector space case. Then we discuss duality for finite abelian groups, which is a sort of analog of Fourier analysis. As an application of duality we show the existence of many injective modules over a ring.

(The lecture is a bit longer than usual because I forgot to stop in the middle.)


For the other lectures in the course see youtube.com/playlist?list=PL8yHsr3EFj52XDLrmvrFDgwcf6XOm2TEE