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Derek Holt
Derek Holt
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clyb
clyb
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For anya ring R, does GL$GL_n(R)$ embed into GL$GL_m(F)$ for some field F?

For anySuppose $R$ is a noncommutative ring R, does. What is the sufficient and necessary condition for $GL(R)$ embed$GL_n(R)$ embedding into $GL(F)$$GL_m(F)$ for some field F$F$?

In particular, what if $R$ is the group ring $\mathbb{Z}D_8$ or $\mathbb{Z}_2[D_8,t^{\pm1}]$, where $D_8$ is the dihedral group of order 8.

Thanks!.

For any ring R, does GL(R) embed into GL(F) for some field F?

For any ring R, does $GL(R)$ embed into $GL(F)$ for some field F?

For a ring R, does $GL_n(R)$ embed into $GL_m(F)$ for some field F?

Suppose $R$ is a noncommutative ring. What is the sufficient and necessary condition for $GL_n(R)$ embedding into $GL_m(F)$ for some field $F$?

In particular, what if $R$ is the group ring $\mathbb{Z}D_8$ or $\mathbb{Z}_2[D_8,t^{\pm1}]$, where $D_8$ is the dihedral group of order 8.

Thanks!.

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clyb
clyb
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For any ring R, does GL(R) embed into GL(F) for some field F?

For any ring R, does $GL(R)$ embed into $GL(F)$ for some field F?