Tiled orders of finite global dimension

Author:
Hisaaki Fujita

Journal:
Trans. Amer. Math. Soc. **322** (1990), 329-341

MSC:
Primary 16H05; Secondary 16E10

DOI:
https://doi.org/10.1090/S0002-9947-1990-0968884-4

Erratum:
Trans. Amer. Math. Soc. **327** (1991), 919-920.

MathSciNet review:
968884

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Abstract | References | Similar Articles | Additional Information

Abstract: We define a projective link between maximal ideals, with respect to which an idealizer preserves being of finite global dimension. Let be a local Dedekind domain with the quotient ring . We show that for , every tiled -order of finite global dimension in is obtained by iterating idealizers w.r.t. projective links from a hereditary order. For , we give a tiled -order in without this property, which is also a counterexample to Tarsy's conjecture, saying that the maximum finite global dimension of such an order is .

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DOI:
https://doi.org/10.1090/S0002-9947-1990-0968884-4

Article copyright:
© Copyright 1990
American Mathematical Society