Abstract
We ask for practical conditions for two rings \(A\) and \(B\) to have equivalent module categories \(A\)-\(\textit{Mod}\simeq \) \(B\)-\(\textit{Mod}\). This question was completely solved in the 1950s by K. Morita and we present this result here. As application we give Puig theorem of nilpotent blocks, Gabriel’s theorem of the presentation of finite dimensional algebras by quiver and relations and a short introduction to Picard groups of algebras.
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Zimmermann, A. (2014). Morita Theory. In: Representation Theory. Algebra and Applications, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-07968-4_4
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DOI: https://doi.org/10.1007/978-3-319-07968-4_4
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