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Sep 11, 2012 at 23:07 comment added Marty Using Dieudonne's wonderful determinant, taking values in the abelian quotient $Z = K^\times / [K^\times, K^\times]$, characterized by the axioms that say that scaling a row by $z$ scales the determinant by the image of $z$ in $Z$, switching rows or columns changes the sign of the determinant, and adding one row or column to another leaves the determinant unchanged.
Sep 11, 2012 at 21:09 comment added YCor How do you define $SL_n(K)$ when $K$ is not commutative?
Sep 11, 2012 at 19:46 vote accept Vipul Naik
Sep 11, 2012 at 15:30 history edited Mikhail Borovoi CC BY-SA 3.0
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Sep 11, 2012 at 15:23 history edited Mikhail Borovoi CC BY-SA 3.0
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Sep 11, 2012 at 14:22 history answered Mikhail Borovoi CC BY-SA 3.0