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Semiprimary hereditary algebras


Author: Abraham Zaks
Journal: Trans. Amer. Math. Soc. 154 (1971), 129-135
MSC: Primary 16.90
DOI: https://doi.org/10.1090/S0002-9947-1971-0276277-9
MathSciNet review: 0276277
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Abstract: Let $ \Sigma $ be a semiprimary k-algebra, with radical M. If $ \Sigma $ admits a splitting then $ {\dim _k}\Sigma /M \leqq {\dim _k}\Sigma $. The residue algebra $ \Sigma /{M^2}$ is finite (cohomological) dimensional if and only if all residue algebras are finite dimensional. If $ {\dim _k}\Sigma = 1$ then all residue algebras are finite dimensional.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0276277-9
Keywords: Semiprimary hereditary algebra, splitting of a ring, finite dimensional algebra, separable algebra, ring of triangular matrices
Article copyright: © Copyright 1971 American Mathematical Society

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