Iyama's finiteness theorem via strongly quasi-hereditary algebras

Ringel CM (2010)
Journal of Pure and Applied Algebra 214(9): 1687-1692.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Let Lambda be an artin algebra and X a finitely generated Lambda-module. Iyama has shown that there exists a Module Y such that the endomorphism ring Gamma of X circle times Y is quasi-hereditary, with a heredity chain of length n, and that the global dimension of Gamma is bounded by this n. In general, one only knows that a quasi-hereditary algebra with a heredity chain of length It must have global dimension at most 2n - 2. We want to show that Iyama's better bound is related to the fact that the ring Gamma lie constructs is not only quasi-hereditary, but even left strongly quasi-hereditary. By definition, the left strongly quasi-hereditary algebras are the quasi-hereditary algebras with all standard left modules of projective dimension at most 1. (C) 2009 Elsevier B.V. All rights reserved.
Erscheinungsjahr
2010
Zeitschriftentitel
Journal of Pure and Applied Algebra
Band
214
Ausgabe
9
Seite(n)
1687-1692
ISSN
0022-4049
Page URI
https://pub.uni-bielefeld.de/record/1796525

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Ringel CM. Iyama's finiteness theorem via strongly quasi-hereditary algebras. Journal of Pure and Applied Algebra. 2010;214(9):1687-1692.
Ringel, C. M. (2010). Iyama's finiteness theorem via strongly quasi-hereditary algebras. Journal of Pure and Applied Algebra, 214(9), 1687-1692. doi:10.1016/j.jpaa.2009.12.012
Ringel, C. M. (2010). Iyama's finiteness theorem via strongly quasi-hereditary algebras. Journal of Pure and Applied Algebra 214, 1687-1692.
Ringel, C.M., 2010. Iyama's finiteness theorem via strongly quasi-hereditary algebras. Journal of Pure and Applied Algebra, 214(9), p 1687-1692.
C.M. Ringel, “Iyama's finiteness theorem via strongly quasi-hereditary algebras”, Journal of Pure and Applied Algebra, vol. 214, 2010, pp. 1687-1692.
Ringel, C.M.: Iyama's finiteness theorem via strongly quasi-hereditary algebras. Journal of Pure and Applied Algebra. 214, 1687-1692 (2010).
Ringel, Claus Michael. “Iyama's finiteness theorem via strongly quasi-hereditary algebras”. Journal of Pure and Applied Algebra 214.9 (2010): 1687-1692.

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