# noetherian

A module $M$ is if it satisfies the following equivalent conditions:

A ring $R$ is left noetherian if it is noetherian as a left module over itself (i.e. if ${}_{R}R$ is a ), and right noetherian if it is noetherian as a right module over itself (i.e. if $R_{R}$ is an ), and simply noetherian if both conditions hold.

Title noetherian Noetherian 2013-03-22 12:26:53 2013-03-22 12:26:53 antizeus (11) antizeus (11) 5 antizeus (11) Definition msc 16P40 left noetherian right noetherian Artinian Noetherian HollowMatrixRings