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Fundamentalnaya i Prikladnaya Matematika, 2005, Volume 11, Issue 3, Pages 173–187
(Mi fpm839)
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Infinite rank representations of orders in nonsemisimple algebras, and module categories
W. Rump University of Stuttgart
Abstract:
Let $R$ be a Dedekind domain with quotient field $K$ and let $\Lambda$ be an $R$-order in a finite-dimensional $K$-algebra $A$ such that $A/\operatorname{Rad}A$ is separable. We show that if $A$ is not semisimple, then there exists a maximal $R$-order $\Delta$ in a skew-field such that the category $\Lambda\text{-}\mathbf{Lat}$ of $R$-projective $\Lambda$-modules admits a full module category $\Delta\text{-}\mathbf{Mod}$ as a subfactor.
Citation:
W. Rump, “Infinite rank representations of orders in nonsemisimple algebras, and module categories”, Fundam. Prikl. Mat., 11:3 (2005), 173–187; J. Math. Sci., 144:2 (2007), 3993–4003
Linking options:
https://www.mathnet.ru/eng/fpm839 https://www.mathnet.ru/eng/fpm/v11/i3/p173
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Abstract page: | 335 | Full-text PDF : | 100 | References: | 43 | First page: | 1 |
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