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A division ring is a possibly noncommutative ring where every nonzero element has a two-sided multiplicative inverse.

10 votes

Proof a Weyl Algebra isn't isomorphic to a matrix ring over a division ring

A different proof would be to show that a Weyl algebra is not semisimple, that is, that it is not a direct sum of simple submodules as a left module over itself. However, note that there is an infini …
Greg Muller's user avatar