Talk:Matrix ring

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Mathematics rating:	Stub Class	Low Priority	Field: Algebra
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 20:57, 21 May 2007 (UTC)

[edit] How to unstubbify?

Probably a significant amount of matrix rings over division rings should just be covered under the Artin-Wedderburn theorem or semisimple ring or so.

Identification of rings as matrix rings is relatively interesting. For instance, if M_n(R) =~ M_m(S), must m=n or R=~S? A good reference for interesting items to add along these lines is Lam's Modules and Rings, the first chapter in the Morita equivalence section. I think this might be the main hope.

One could certainly add some trivial Morita corollaries to the properties list, but that only makes the article longer, not less stubby. One could link to the Jacobson density theorem which says rings with faithful primitive modules (like Matrix rings over division rings) are very nearly matrix rings over division rings.

One could link to Brauer group or Central simple algebra where matrix rings play the role of the identity element or trivial example, but again this is mostly an Artinian simple ring thing. JackSchmidt 23:34, 3 December 2007 (UTC)