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formatting, added tag (the question was bumped anyway)
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YCor
YCor
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For which rings R$R$ is SL_n$\mathrm{SL}_n(R)$ generated by transvections?

Let $R$ be a commutative ring $R$ with $1$, and $n \geq 2$ an integer.

Under which conditions is the group $SL_n(R)$$\operatorname{SL}_n(R)$ generated by transvections?

(A transvection is a matrix with $1$ everywhere on the diagonal and exactly one other non-zero entry.) This is certainly the case if $R$ is a field, or if $R$ is a Euclidean domain, but I'm wondering whether there is a complete answer to the question.

For which rings R is SL_n(R) generated by transvections?

Let $R$ be a commutative ring $R$ with $1$, and $n \geq 2$ an integer.

Under which conditions is the group $SL_n(R)$ generated by transvections?

(A transvection is a matrix with $1$ everywhere on the diagonal and exactly one other non-zero entry.) This is certainly the case if $R$ is a field, or if $R$ is a Euclidean domain, but I'm wondering whether there is a complete answer to the question.

For which rings $R$ is $\mathrm{SL}_n(R)$ generated by transvections?

Let $R$ be a commutative ring $R$ with $1$, and $n \geq 2$ an integer.

Under which conditions is the group $\operatorname{SL}_n(R)$ generated by transvections?

(A transvection is a matrix with $1$ everywhere on the diagonal and exactly one other non-zero entry.) This is certainly the case if $R$ is a field, or if $R$ is a Euclidean domain, but I'm wondering whether there is a complete answer to the question.

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Tom De Medts
Tom De Medts
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For which rings R is SL_n(R) generated by transvections?

Let $R$ be a commutative ring $R$ with $1$, and $n \geq 2$ an integer.

Under which conditions is the group $SL_n(R)$ generated by transvections?

(A transvection is a matrix with $1$ everywhere on the diagonal and exactly one other non-zero entry.) This is certainly the case if $R$ is a field, or if $R$ is a Euclidean domain, but I'm wondering whether there is a complete answer to the question.