Quasi-heredity of algebras and their factor algebras

Xi, Chang Chang

doi:10.1090/S0002-9939-1993-1154251-8

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Quasi-heredity of algebras and their factor algebras
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by Chang Chang Xi

Proc. Amer. Math. Soc. 119 (1993), 727-729

DOI: https://doi.org/10.1090/S0002-9939-1993-1154251-8

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Abstract:

Let $A$ be a finite-dimensional algebra over an algebraically closed field and denote by $N$ the Jacobson radical of $A$. If there is an integer $i \geqslant 2$ such that $A/{N^i}$ is quasi-hereditary, then $A$ is quasi-hereditary.

References

Vlastimil Dlab and Claus Michael Ringel, Quasi-hereditary algebras, Illinois J. Math. 33 (1989), no. 2, 280–291. MR 987824
Chang Chang Xi, The structure of Schur algebras $S_k(n,p)$ for $n\geq p$, Canad. J. Math. 44 (1992), no. 3, 665–672. MR 1176375, DOI 10.4153/CJM-1992-040-5