prime ringPrimeRing2001-10-20 02:21:332007-11-10 00:34:04Definition\usepackage{amssymb}
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\usepackage{xypic}A ring $R$ is said to be a \emph{prime ring} if the zero ideal is a prime ideal.
If a prime ring $R$ is commutative, then it is a cancellation ring. If in \PMlinkescapetext{addition} $R$ has a multiplicative identity $1 \neq 0$, then it is an integral domain.