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Stable equivalence for self-injective algebras and a generalization of tilting modules. (English) Zbl 0726.16009
Let T(A) denote the trivial extension \(A\ltimes DA\) of an Artin algebra A by the minimal injective cogenerator DA. The main results state that for an equivalence S: mod-T(A)\(=mod\)-T(B) with two additional conditions there is a generalized tilting bimodule \({}_ BT_ A\) where A and B are Artin algebras. Several interesting properties of generalized tilting modules are also obtained as well as a construction of a stably equivalent functor.

MSC:
16G10 Representations of associative Artinian rings
16D90 Module categories in associative algebras
16D50 Injective modules, self-injective associative rings
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