On a Duality Theorem of Wakamatsu
نویسنده
چکیده
Let R be a left coherent ring, S a right coherent ring and RU a generalized tilting module, with S = End(RU ) satisfying the condition that each finitely presented left R-module X with ExtR(X,U )= 0 for any i ≥ 1 is U -torsionless. If M is a finitely presented left R-module such that ExtR(M,U )= 0 for any i ≥ 0 with i 6= n (where n is a nonnegative integer), then ExtS(Ext n R(M,U ),U ) ∼= M and ExtS(Ext n R(M,U ),U )= 0 for any i ≥ 0 with i 6= n. A duality is thus induced between the category of finitely presented holonomic left R-modules and the category of finitely presented holonomic right S-modules. 2000 Mathematics subject classification: 16E30, 16D90.
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