Geodesic
Diagonal reductions of matrices over exchange ideals
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 9-18 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $U_1V_1AU_2V_2= \operatorname{diag}(e_1,\cdots ,e_n)$ for idempotents $e_1,\cdots ,e_n\in I$.
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 $U_1V_1AU_2V_2= \operatorname{diag}(e_1,\cdots ,e_n)$ for idempotents $e_1,\cdots ,e_n\in I$.
Classification : 15A21, 16D25, 16D70, 16E20, 16E50, 16U60, 16U99
Keywords: exchange ring; ideal; related comparability 
@article{CMJ_2006_56_1_a1,
     author = {Chen, Huanyin},
     title = {Diagonal reductions of matrices over exchange ideals},
     journal = {Czechoslovak Mathematical Journal},
     pages = {9--18},
     year = {2006},
     volume = {56},
     number = {1},
     mrnumber = {2206283},
     zbl = {1157.16302},
     language = {en},
     url = {http://geodesic.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. http://geodesic.mathdoc.fr/item/CMJ_2006_56_1_a1/