Whitehead groups of exchange rings with primitive factors artinian
We show that if R is an exchange ring with primitive factors artinian then K1(R)≅U(R)/V(R), where U(R) is the group of units of R and V(R) is the subgroup generated by {(1+ab)(1+ba)−1|a,b∈R with 1+ab∈U(R)}. As a corollary, K1(R) is the abelianized group of units of R if 1/2∈R....
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201005464 |
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| _version_ | 1849414824069431296 |
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| author | Huanyin Chen Fu-an Li |
| author_facet | Huanyin Chen Fu-an Li |
| author_sort | Huanyin Chen |
| collection | DOAJ |
| description | We show that if R is an exchange ring with primitive factors artinian then K1(R)≅U(R)/V(R), where U(R) is the group of units of R and V(R) is the subgroup generated by {(1+ab)(1+ba)−1|a,b∈R with 1+ab∈U(R)}. As a corollary, K1(R) is the abelianized group of units of R if 1/2∈R. |
| format | Article |
| id | doaj-art-72464d9c4fdc4b36a0ebe99010f974f2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-72464d9c4fdc4b36a0ebe99010f974f22025-08-20T03:33:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0126739339810.1155/S0161171201005464Whitehead groups of exchange rings with primitive factors artinianHuanyin Chen0Fu-an Li1Department of Mathematics, Hunan Normal University, Changsha 410006, ChinaInstitute of Mathematics, Chinese Academy of Sciences, Beijing 100080, ChinaWe show that if R is an exchange ring with primitive factors artinian then K1(R)≅U(R)/V(R), where U(R) is the group of units of R and V(R) is the subgroup generated by {(1+ab)(1+ba)−1|a,b∈R with 1+ab∈U(R)}. As a corollary, K1(R) is the abelianized group of units of R if 1/2∈R.http://dx.doi.org/10.1155/S0161171201005464 |
| spellingShingle | Huanyin Chen Fu-an Li Whitehead groups of exchange rings with primitive factors artinian International Journal of Mathematics and Mathematical Sciences |
| title | Whitehead groups of exchange rings with primitive factors artinian |
| title_full | Whitehead groups of exchange rings with primitive factors artinian |
| title_fullStr | Whitehead groups of exchange rings with primitive factors artinian |
| title_full_unstemmed | Whitehead groups of exchange rings with primitive factors artinian |
| title_short | Whitehead groups of exchange rings with primitive factors artinian |
| title_sort | whitehead groups of exchange rings with primitive factors artinian |
| url | http://dx.doi.org/10.1155/S0161171201005464 |
| work_keys_str_mv | AT huanyinchen whiteheadgroupsofexchangeringswithprimitivefactorsartinian AT fuanli whiteheadgroupsofexchangeringswithprimitivefactorsartinian |