# minimal prime ideal

A prime ideal $P$ of a ring $R$ is called a minimal prime ideal if it does not properly contain any other prime ideal of $R$.

If $R$ is a prime ring, then the zero ideal is a prime ideal, and is thus the unique minimal prime ideal of $R$.

Title minimal prime ideal MinimalPrimeIdeal 2013-03-22 12:01:21 2013-03-22 12:01:21 antizeus (11) antizeus (11) 6 antizeus (11) Definition msc 16D80 ZeroIdeal