| Title:
|
Diagonal reductions of matrices over exchange ideals (English) |
| Author:
|
Chen, Huanyin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
9-18 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $e_1,\cdots ,e_n\in I$. (English) |
| Keyword:
|
exchange ring |
| Keyword:
|
ideal |
| Keyword:
|
related comparability |
| MSC:
|
15A21 |
| MSC:
|
16D25 |
| MSC:
|
16D70 |
| MSC:
|
16E20 |
| MSC:
|
16E50 |
| MSC:
|
16U60 |
| MSC:
|
16U99 |
| idZBL:
|
Zbl 1157.16302 |
| idMR:
|
MR2206283 |
| . |
| Date available:
|
2009-09-24T11:31:07Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128050 |
| . |
| Reference:
|
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| Reference:
|
[2] P. Ara, K. R. Goodearl, K. C. O’Meara and E. Pardo: Diagonalization of matrices over regular rings.Linear Algebra Appl. 265 (1997), 147–163. MR 1466896 |
| Reference:
|
[3] P. Ara, K. R. Goodearl, K. C. O’Meara and E. Pardo: Separative cancellation for projective modules over exchange rings.Israel J. Math. 105 (1998), 105–137. MR 1639739, 10.1007/BF02780325 |
| Reference:
|
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| Reference:
|
[5] H. Chen: Elements in one-sided unit regular rings.Comm. Algebra 25 (1997), 2517–2529. Zbl 0881.16004, MR 1459573, 10.1080/00927879708826002 |
| Reference:
|
[6] H. Chen: Exchange rings, related comparability and power-substitution.Comm. Algebra 26 (1998), 3383–3668. Zbl 0914.16001, MR 1641632, 10.1080/00927879808826347 |
| Reference:
|
[7] H. Chen: Related comparability over exchange rings.Comm. Algebra 27 (1999), 4209–4216. Zbl 0952.16010, MR 1705862, 10.1080/00927879908826691 |
| Reference:
|
[8] H. Chen: Generalized stable regular rings.Comm. Algebra 31 (2003), 4899–4910. Zbl 1050.16005, MR 1998034, 10.1081/AGB-120023138 |
| Reference:
|
[9] H. Chen and M. Chen: Generalized ideal-stable regular rings.Comm. Algebra 31 (2003), 4989–5001. MR 1998039, 10.1081/AGB-120023143 |
| Reference:
|
[10] K. R. Goodearl: Von Neumann Regular Rings.Pitman, London, San Francisco, Melbourne, 1979, second ed., Krieger, Malabar, Fl., 1991. Zbl 0749.16001, MR 0533669 |
| . |
