Diagonal reductions of matrices over exchange ideals

Chen, Huanyin

Geodesic

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Diagonal reductions of matrices over exchange ideals

Chen, Huanyin

Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 9-18.

Voir la notice de l'article dans Czech Digital Mathematics Library

Résumé

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 \in M_{n} (I)

, there exist left invertible

U_{1}, U_{2} \in M_{n} (R)

and right invertible

V_{1}, V_{2} \in M_{n} (R)

such that

U_{1} V_{1} A U_{2} V_{2} = diag (e_{1}, \dots, e_{n})

for idempotents

e_{1}, \dots, e_{n} \in I

MR Zbl

Classification : 15A21, 16D25, 16D70, 16E20, 16E50, 16U60, 16U99
Mots-clés : exchange ring; ideal; related comparability

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     author = {Chen, Huanyin},
     title = {Diagonal reductions of matrices over exchange ideals},
     journal = {Czechoslovak Mathematical Journal},
     pages = {9--18},
     publisher = {mathdoc},
     volume = {56},
     number = {1},
     year = {2006},
     mrnumber = {2206283},
     zbl = {1157.16302},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/CMJ_2006__56_1_a1/}
}

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Chen, Huanyin. Diagonal reductions of matrices over exchange ideals. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 9-18. https://geodesic-test.mathdoc.fr/item/CMJ_2006__56_1_a1/