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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Tiled orders of finite global dimension

Author: Hisaaki Fujita
Journal: Trans. Amer. Math. Soc. 322 (1990), 329-341
MSC: Primary 16H05; Secondary 16E10
Erratum: Trans. Amer. Math. Soc. 327 (1991), 919-920.
MathSciNet review: 968884
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Abstract: We define a projective link between maximal ideals, with respect to which an idealizer preserves being of finite global dimension. Let $ D$ be a local Dedekind domain with the quotient ring $ K$. We show that for $ 2 \leq n \leq 5$, every tiled $ D$-order of finite global dimension in $ {(K)_n}$ is obtained by iterating idealizers w.r.t. projective links from a hereditary order. For $ n \geq 6$, we give a tiled $ D$-order in $ {(K)_n}$ without this property, which is also a counterexample to Tarsy's conjecture, saying that the maximum finite global dimension of such an order is $ n - 1$.

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Article copyright: © Copyright 1990 American Mathematical Society

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