Mathematics – Rings and Algebras
Scientific paper
2002-03-18
Mathematics
Rings and Algebras
43 pages, Latex, to appear in Advances in Math. Result on finite global dimension added, other minor changes
Scientific paper
We study a class of noncommutative surfaces and their higher dimensional analogues which provide answers to several open questions in noncommutative projective geometry. Specifically, we give the first known graded algebras which are noetherian but not strongly noetherian, answering a question of Artin, Small, and Zhang. In addition, these examples are maximal orders and satisfy the $\chi_1$ condition but not $\chi_i$ for $i \geq 2$, answering a questions of Stafford and Zhang and a question of Stafford and Van den Bergh. Finally, we show that these algebras have finite cohomological dimension.
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