| Title:
|
Exchange rings in which all regular elements are one-sided unit-regular (English) |
| Author:
|
Chen, Huanyin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
899-910 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be an exchange ring in which all regular elements are one-sided unit-regular. Then every regular element in $R$ is the sum of an idempotent and a one-sided unit. Furthermore, we extend this result to exchange rings satisfying related comparability. (English) |
| Keyword:
|
exchange ring |
| Keyword:
|
one-sided unit-regularity |
| Keyword:
|
idempotent |
| MSC:
|
16D70 |
| MSC:
|
16E20 |
| MSC:
|
16E50 |
| MSC:
|
16U60 |
| MSC:
|
16U99 |
| idZBL:
|
Zbl 1166.16004 |
| idMR:
|
MR2471155 |
| . |
| Date available:
|
2010-07-21T08:04:21Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140429 |
| . |
| Reference:
|
[1] Ara, P.: Strongly $\pi$-regular rings have stable range one.Proc. Amer. Math. Soc. 124 (1996), 3293-3298. Zbl 0865.16007, MR 1343679, 10.1090/S0002-9939-96-03473-9 |
| Reference:
|
[2] Ara, P.: The exchange property for purely infinite simple rings.Proc. Amer. Math. Soc. 132 (2004), 2543-2547. Zbl 1055.16012, MR 2054778, 10.1090/S0002-9939-04-07369-1 |
| Reference:
|
[3] Ara, P., Goodearl, K. R., O'Meara, K. C., Pardo, E.: Separative cancellation for projective modules over exchange rings.Israel J. Math. 105 (1998), 105-137. Zbl 0908.16002, MR 1639739, 10.1007/BF02780325 |
| Reference:
|
[4] Ara, P., Goodearl, K. R., Pardo, E.: $K_0$ of purely infinite simple regular rings.$K$-Theory 26 (2002), 69-100. Zbl 1012.16013, MR 1918211, 10.1023/A:1016358107918 |
| Reference:
|
[5] Camillo, V. P., Khurana, D. A.: Characterization of unit regular rings.Comm. Algebra 29 (2001), 2293-2295. Zbl 0992.16011, MR 1837978, 10.1081/AGB-100002185 |
| Reference:
|
[6] Chen, H.: Elements in one-sided unit regular rings.Comm. Algebra 25 (1997), 2517-2529. Zbl 0881.16004, MR 1459573, 10.1080/00927879708826002 |
| Reference:
|
[7] Chen, H.: Related comparability over exchange rings.Comm. Algebra 27 (1999), 4209-4216. Zbl 0952.16010, MR 1705862, 10.1080/00927879908826691 |
| Reference:
|
[8] Chen, H.: Regular rings, idempotents and products of one-sided units.Comm. Algebra 34 (2006), 737-741. Zbl 1100.16009, MR 2211952, 10.1080/00927870500388026 |
| Reference:
|
[9] Chen, H., Li, F.: Exchange rings satisfying related comparability.Collect. Math. 53 (2002), 157-164. MR 1913515 |
| Reference:
|
[10] Khurana, D., Lam, T. Y.: Clean matrices and unit-regular matrices.J. Algebra 280 (2004), 683-698. Zbl 1067.16050, MR 2090058, 10.1016/j.jalgebra.2004.04.019 |
| Reference:
|
[11] Lam, T. Y.: A crash course on stable range, cancellation, substitution and exchange.J. Algebra Appl. 3 (2004), 301-343. Zbl 1072.16013, MR 2096452, 10.1142/S0219498804000897 |
| Reference:
|
[12] Lu, D., Li, Q., Tong, W.: Comparability, stability, and completions of ideals.Comm. Algebra 32 (2004), 2617-2634. Zbl 1074.16007, MR 2099921, 10.1081/AGB-120037403 |
| Reference:
|
[13] Nicholson, W. K., Zhou, Y.: Clean rings: A survey, Advances in Ring Theory.Proceedings of the 4th China-Japan-Korea International Conference (2004), 181-198. MR 2181857 |
| Reference:
|
[14] Pardo, E.: Comparability, separativity, and exchange rings.Comm. Algebra 24 (1996), 2915-2929. Zbl 0859.16001, MR 1396864, 10.1080/00927879608825721 |
| Reference:
|
[15] Wei, J.: Unit-regularity and stable range conditions.Comm. Algebra 33 (2005), 1937-1946. Zbl 1093.16003, MR 2150852, 10.1081/AGB-200063337 |
| Reference:
|
[16] Tuganbaev, A. A.: Rings Close to Regular.Kluwer Academic Publishers, Dordrecht, Boston, London (2002). Zbl 1120.16012, MR 1958361 |
| . |
