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| Linear Group over a Class of Ring R |
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Citation： |
Yuan Bingcheng.Linear Group over a Class of Ring R[J].Chinese Annals of Mathematics B,1985,6(1):35~46 |
| Page view： 676
Net amount： 652 |
Authors： |
Yuan Bingcheng; |
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| Abstract： |
Let R be a commutative ring^[1] with identical element 1 and maximal ideal M_i where i\in N and N is an ordered indieatrix set. Let the mapping
$f:R\rightarrow \prod\limits_{i \in N} {R/{M_i}}$,
be a ring homomorphism from R onto $[\prod\limits_{i \in N} {R/{M_i}} \]$, where $[\prod\limits_{i \in N} {R/{M_i}} \]$ is the direct product of residual fields B/M_i. In this paper, it is proved that if A \in GL_n(R), then A=BH_1……H_k-1,
where res B=1 and H_1,\cdots, H_k-1 are the symmetries. Furthermore, the bound of the positive integer number K is investigated. In particular, the author gives the smallest number l(A) of symmetric factors in the products which expresses the elements of G_n= {A\in GLn(R)| det A=±l}. Consequently, the l(A) problems discussed in [2, 3, 4] are special cases of this paper. |
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