Abstract
Let R be a discrete valuation ring with residue class field F. For an arbitrary prime p, we construct a tiled R-order Λ such that global dimension gld Λ = 5 if characteristic char F ≠ p and gld Λ = ∞ if char F = p. If char F ≠ p, Λ is a tiled R-order of finite global dimension with no neat primitive idempotent, so that a question posed in Fujita (Citation2002) is solved.
ACKNOWLEDGMENTS
The authors would like to thank the referee for helpful comments to improve the article. The first-named author was partially supported by JSPS Grant-in-Aid for Scientific Research ((C) 18540011).
Notes
Communicated by J. Kuzmanovich.