Diagonal reductions of matrices over exchange ideals
Czechoslovak Mathematical Journal (2006)
- Volume: 56, Issue: 1, page 9-18
- ISSN: 0011-4642
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topChen, Huanyin. "Diagonal reductions of matrices over exchange ideals." Czechoslovak Mathematical Journal 56.1 (2006): 9-18. <http://eudml.org/doc/31013>.
@article{Chen2006,
abstract = {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 $e_1,\cdots ,e_n\in I$.},
author = {Chen, Huanyin},
journal = {Czechoslovak Mathematical Journal},
keywords = {exchange ring; ideal; related comparability; exchange rings; exchange ideals; related comparability; idempotents},
language = {eng},
number = {1},
pages = {9-18},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Diagonal reductions of matrices over exchange ideals},
url = {http://eudml.org/doc/31013},
volume = {56},
year = {2006},
}
TY - JOUR
AU - Chen, Huanyin
TI - Diagonal reductions of matrices over exchange ideals
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 1
SP - 9
EP - 18
AB - 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 $e_1,\cdots ,e_n\in I$.
LA - eng
KW - exchange ring; ideal; related comparability; exchange rings; exchange ideals; related comparability; idempotents
UR - http://eudml.org/doc/31013
ER -
References
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