# Diagonal reductions of matrices over exchange ideals

Czechoslovak Mathematical Journal (2006)

- Volume: 56, Issue: 1, page 9-18
- ISSN: 0011-4642

## Access Full Article

top## Abstract

top## How to cite

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

top- Stability properties of exchange rings, Birkenmeier G. F. (ed.) et al., International symposium on ring theory. Boston, MA: Birkhäuser. Trends in Mathematics, 2001, pp. 23–42. (2001) Zbl0979.16001MR1851191
- Diagonalization of matrices over regular rings, Linear Algebra Appl. 265 (1997), 147–163. (1997) MR1466896
- 10.1007/BF02780325, Israel J. Math. 105 (1998), 105–137. (1998) MR1639739DOI10.1007/BF02780325
- 10.1006/jabr.2000.8330, J. Algebra 230 (2000), 608–655. (2000) MR1775806DOI10.1006/jabr.2000.8330
- 10.1080/00927879708826002, Comm. Algebra 25 (1997), 2517–2529. (1997) Zbl0881.16004MR1459573DOI10.1080/00927879708826002
- 10.1080/00927879808826347, Comm. Algebra 26 (1998), 3383–3668. (1998) Zbl0914.16001MR1641632DOI10.1080/00927879808826347
- 10.1080/00927879908826691, Comm. Algebra 27 (1999), 4209–4216. (1999) Zbl0952.16010MR1705862DOI10.1080/00927879908826691
- 10.1081/AGB-120023138, Comm. Algebra 31 (2003), 4899–4910. (2003) Zbl1050.16005MR1998034DOI10.1081/AGB-120023138
- 10.1081/AGB-120023143, Comm. Algebra 31 (2003), 4989–5001. (2003) MR1998039DOI10.1081/AGB-120023143
- Von Neumann Regular Rings, Pitman, London, San Francisco, Melbourne, 1979, second ed., Krieger, Malabar, Fl., 1991. (1991) Zbl0749.16001MR0533669

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.