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Diagonal reductions of matrices over exchange ideals

Huanyin Chen (2006)

Czechoslovak Mathematical Journal

In this paper, we introduce related comparability for exchange ideals. Let I be an exchange ideal of a ring R . If I satisfies related comparability, then for any regular matrix A M n ( I ) , there exist left invertible U 1 , U 2 M n ( R ) and right invertible V 1 , V 2 M n ( R ) such that U 1 V 1 A U 2 V 2 = diag ( e 1 , , e n ) for idempotents e 1 , , e n I .

Dually steady rings

Robert El Bashir, Tomáš Kepka, Jan Žemlička (2011)

Acta Universitatis Carolinae. Mathematica et Physica

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