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Primitive ring
In abstract algebra, a left primitive ring R is a ring with a faithful simple left module R-module. A right primitive ring is defined similarly.
Primitive rings generalize simple rings.
Properties
- Every simple ring is primitive.
- An Artinian ring is primitive if and only if it is simple.
- A commutative ring is primitive if and only if it is a field.
Last updated: 08-29-2005 01:56:33
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details