Tiled orders of finite global dimension

Hisaaki Fujita
1990 Transactions of the American Mathematical Society  
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 :::; n :::; 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 :::: 6, we give a tiled D-order in (K)n without this property, which is also a counterexample to Tarsy's conjecture, saying that
more » ... he maximum finite global dimension of such an order is n -I .
doi:10.1090/s0002-9947-1990-0968884-4 fatcat:ouaaivro4jghndjmrq77bzarfi