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Injective ideals of regular rings. (Chinese. English summary) Zbl 1199.16034

Summary: Let \(R\) be regular, \(A\in M_n(R)\). If \(M_n(R)AM_n(R)\) is injective as a right \(M_n(R)\)-module, we prove that there exist \(U,V\in\text{GL}_n(R)\) such that \(UAV\) is a diagonal matrix.

MSC:

16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16D25 Ideals in associative algebras
16D50 Injective modules, self-injective associative rings
15A21 Canonical forms, reductions, classification
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