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Global dimension of tiled orders over a discrete valuation ring

1974
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Transactions of the American Mathematical Society
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Let R be a discrete valuation ring with maximal ideal m and the quotient field K. Let A = (m ") Ç M (K) be a tiled /{-order, where X.. e Z and X.. =0 for 1 s i s,7». The following results are proved. Theorem 1. There are, up to conjugation, only finitely many tiled R-orders in M"(X) of finite global dimension. Theorem 2. Tiled R-orders in M (K) of finite global dimension satisfy DCC. Theorem 3. Let A CM (/?) and let T be obtained from A by replacing the entries above the main diagonal by

doi:10.1090/s0002-9947-1974-0349729-3
fatcat:zpyyeds275fp5cod7hvzyl7w2q