# artinian

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

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

Title artinian Artinian 2013-03-22 12:26:46 2013-03-22 12:26:46 antizeus (11) antizeus (11) 6 antizeus (11) Definition msc 16D10 left artinian right artinian Noetherian Noetherian2 HollowMatrixRings