Talk:Dieudonné determinant

Unclear abelianization
The article includes this sentence in the Introduction:

"If K is a division ring, then the Dieudonné determinant is a homomorphism of groups from the group GLn(K) of invertible n by n matrices over K onto the abelianization K×/[K×, K×] of the multiplicative group K× of K."

But the linked Abelianization article discusses the meaning of abelianization only in the case of a group, not a division ring.

Can we assume that, in the symbol K×/[K×, K×], the expression [K×, K×] denotes the ideal of the ring generated by all elements of the form xy - yx, where x and y are both nonzero ?

I hope someone knowledgeable about this subject can add the appropriate information to the article. 2601:200:C000:1A0:55D7:C536:B427:8DB0 (talk) 23:23, 3 October 2021 (UTC)