A Noether-Deuring theorem for derived categories. (Q2902687)

The classical Noether-Deuring theorem states that given an algebra \(A\) over a field \(K\) and a finite extension field \(L\) of \(K\), two \(A\)-modules \(M\) and \(N\) are isomorphic if the \(A\otimes_KL\)-modules \(M\otimes_KL\) and \(N\otimes_KL\) are isomorphic. In [Rings, Modules, Radicals. Colloq. Math. Soc. János Bolyai 6, 457-462 (1973; Zbl 0266.13013)], \textit{K. W. Roggenkamp} extended this theorem to certain extensions \(S\) of a commutative ring \(R\) and modules over Noetherian \(R\)-algebras.NEWLINENEWLINE The main result of this paper is a further extension of the Noether-Deuring theorem to complexes over Noetherian \(R\)-algebras and certain extensions \(S\) over a commutative ring \(R\). Roggenkamp's theorem is then recovered as a special case of this main result. This paper also investigates some extensions of the Krull-Schmidt theorem to complexes.