On K2-group of a Formal Matrix Ring
Let S be a formal matrix ring, T the subring consisting of all diagonal elements, I the set consisting of all off-diagonal elements. Then I is a split radical ideal under certain conditions. In this paper, we show that K2（S）≈ K2（T） G K2（S, I）, and a presentation of K2（S, I） is given....
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| Published in | Acta mathematica Sinica. English series Vol. 28; no. 9; pp. 1897 - 1906 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
2012
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| Subjects | |
| Online Access | Get full text |
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| Abstract | Let S be a formal matrix ring, T the subring consisting of all diagonal elements, I the set consisting of all off-diagonal elements. Then I is a split radical ideal under certain conditions. In this paper, we show that K2（S）≈ K2（T） G K2（S, I）, and a presentation of K2（S, I） is given. |
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| AbstractList | Let
S
be a formal matrix ring,
T
the subring consisting of all diagonal elements,
I
the set consisting of all off-diagonal elements. Then
I
is a split radical ideal under certain conditions. In this paper, we show that
K
2
(
s
)≃
K
2
(
T
)⊕
K
2
(
S, I
), and a presentation of
K
2
(
S, I
) is given. Let S be a formal matrix ring, T the subring consisting of all diagonal elements, I the set consisting of all off-diagonal elements. Then I is a split radical ideal under certain conditions. In this paper, we show that K2（S）≈ K2（T） G K2（S, I）, and a presentation of K2（S, I） is given. |
| Author | Zi Qiang FAN Zhi Xiang YIN |
| AuthorAffiliation | Department of Mathematics, Anhui University of Science and Technology, Huainan 232001, P. R. China |
| Author_xml | – sequence: 1 givenname: Zi Qiang surname: Fan fullname: Fan, Zi Qiang email: zqfan71@163.com organization: Department of Mathematics, Anhui University of Science and Technology – sequence: 2 givenname: Zhi Xiang surname: Yin fullname: Yin, Zhi Xiang organization: Department of Mathematics, Anhui University of Science and Technology |
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| Cites_doi | 10.1090/S0002-9904-1975-13894-8 10.1007/s10114-010-7429-8 10.1016/0021-8693(78)90024-8 10.1007/s101149900010 10.1016/0021-8693(85)90100-0 10.1016/0022-4049(77)90007-X |
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| Copyright | Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2012 |
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| Keywords | 19C40 19C20 extension of groups group relative |
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| Notes | Let S be a formal matrix ring, T the subring consisting of all diagonal elements, I the set consisting of all off-diagonal elements. Then I is a split radical ideal under certain conditions. In this paper, we show that K2（S）≈ K2（T） G K2（S, I）, and a presentation of K2（S, I） is given. 11-2039/O1 K2 group, relative K2 group, extension of groups |
| PageCount | 10 |
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| PublicationDate | 2012 9-2012 |
| PublicationDateYYYYMMDD | 2012-01-01 |
| PublicationDate_xml | – year: 2012 text: 2012 |
| PublicationDecade | 2010 |
| PublicationPlace | Heidelberg |
| PublicationPlace_xml | – name: Heidelberg |
| PublicationTitle | Acta mathematica Sinica. English series |
| PublicationTitleAbbrev | Acta. Math. Sin.-English Ser |
| PublicationTitleAlternate | Acta Mathematica Sinica |
| PublicationYear | 2012 |
| Publisher | Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |
| Publisher_xml | – name: Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |
| References | Kolster (CR5) 1984; 353 Milnor (CR1) 1971 Dennis, Geller (CR10) 1976; 56 Fan, Song (CR13) 2007; 31 Kolster (CR4) 1985; 95 Liu, Zhang (CR9) 2010; 26 Maazen, Stienstra (CR7) 1977; 10 Keune (CR8) 1978; 54 Song, Guo (CR11) 2003; 32 Keune (CR3) 1972 Silvester (CR6) 1981 Van der Kallen, Maazen, Stienstra (CR2) 1975; 81 Guo, Li (CR14) 2001; 17 Fan, Song, Chu (CR12) 2006; 36 |
| References_xml | – volume: 81 start-page: 934 year: 1975 end-page: 936 ident: CR2 article-title: A presentation for some ( ) publication-title: Bull. Amer. Math. Soc. doi: 10.1090/S0002-9904-1975-13894-8 contributor: fullname: Stienstra – volume: 353 start-page: 132 year: 1984 end-page: 164 ident: CR5 article-title: General symbols and presentations of elementary linear groups publication-title: J. Reine Angew. Math. contributor: fullname: Kolster – volume: 26 start-page: 2231 issue: 11 year: 2010 end-page: 2238 ident: CR9 article-title: Principal quasi-Baerness of formal power series rings publication-title: Acta Mathematica Sinica, English Series doi: 10.1007/s10114-010-7429-8 contributor: fullname: Zhang – volume: 56 start-page: 73 year: 1976 end-page: 78 ident: CR10 article-title: of upper triangular matrix rings publication-title: Proc. Amer. Math. Soc. contributor: fullname: Geller – volume: 54 start-page: 159 year: 1978 end-page: 177 ident: CR8 article-title: The relativization of publication-title: J. Algebra doi: 10.1016/0021-8693(78)90024-8 contributor: fullname: Keune – year: 1971 ident: CR1 article-title: Introduction to Algebraic K-Theory publication-title: Annals of Math. Studies, Vol. 72 contributor: fullname: Milnor – volume: 32 start-page: 195 year: 2003 end-page: 200 ident: CR11 article-title: On group of semiperfect rings (in Chinese) publication-title: Adv. in Math. contributor: fullname: Guo – volume: 17 start-page: 273 issue: 2 year: 2001 end-page: 276 ident: CR14 article-title: group of finite-dimensional path algebra publication-title: Acta Mathematica Sinica, English Series doi: 10.1007/s101149900010 contributor: fullname: Li – year: 1981 ident: CR6 publication-title: Introduction to Algebraic K-Theory contributor: fullname: Silvester – volume: 36 start-page: 720 issue: 7 year: 2006 end-page: 726 ident: CR12 article-title: On relative -groups of semiperfect rings (in Chinese) publication-title: J. of Univ. of Sci. and Tech. of China contributor: fullname: Chu – volume: 31 start-page: 469 year: 2007 end-page: 493 ident: CR13 article-title: On relative -groups of semiperfect rings publication-title: Southeast Asian Bulletin of Mathematics contributor: fullname: Song – start-page: 281 year: 1972 end-page: 303 ident: CR3 publication-title: The of 1-fold ring. Lecture Notes in Math., Vol. 342 contributor: fullname: Keune – volume: 95 start-page: 173 year: 1985 end-page: 200 ident: CR4 article-title: of non-commutative local rings publication-title: J. Algebra doi: 10.1016/0021-8693(85)90100-0 contributor: fullname: Kolster – volume: 10 start-page: 271 year: 1977 end-page: 294 ident: CR7 article-title: A presentation for of split radical pairs publication-title: J. Pure Appl. Algebra doi: 10.1016/0022-4049(77)90007-X contributor: fullname: Stienstra |
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| Snippet | Let S be a formal matrix ring, T the subring consisting of all diagonal elements, I the set consisting of all off-diagonal elements. Then I is a split radical... Let S be a formal matrix ring, T the subring consisting of all diagonal elements, I the set consisting of all off-diagonal elements. Then I is a split radical... |
| SourceID | springer chongqing |
| SourceType | Publisher |
| StartPage | 1897 |
| SubjectTerms | Mathematics Mathematics and Statistics 元素组成 分裂 子环 对角线 演示 理想 矩阵环 集合 |
| Title | On K2-group of a Formal Matrix Ring |
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