Subrings of Artinian and Noetherian Rings
نویسنده
چکیده
An easy consequence of this is that a left Noetherian (respectively left Artinian) ring which is finitely generated over its center is right Noetherian (respectively right Artinian). Theorem 1 follows easily from Theorem 2, which gives a partial converse to the following standard fact: IfR C S are rings, and ifQ is an injective R-module, then Hom~(S, Q) is an injective S-module (this follows, for example, from [2: II.6, Eq. (4)]).
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