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matrix ring

Defines: 
matrix group
Type of Math Object: 
Definition
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

16S50 no label found

Comments

I wonder then if the "n" in question here shouldn't be built in to the definition of a matrix ring (i.e. a \emph{matrix ring of level $n$} or something). That every ring is a matrix ring, and every matrix ring is a ring, makes the definition (though not the idea) pretty useless. As you point out in the article, interesting questions are not "Is this ring a matrix ring," which has a trivial answer, but instead (in my ad hoc definition above) things like "Is this ring a matrix ring of order 2?"

Cam

I see your point. But a 1x1 matrix, as useless as it sounds, is still a mathematically valid construct. So instead of requiring n>1, any ring that is not an isomorphic image of M_n(S) with n>1 is called a trivial matrix ring. The entry is revised to reflect this.

Chi

Okay, I think that's a fine fix.

Cam

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