The Extension of the Noetherian Conditions for Matrix

Abstract

Let be a ring and is a set of matrix with the entries of the matrix element of ring . Set
of matrix together with addition and multiplication matrix is matrix ring. Noetherian is condition of ring (resp.
module) which are every ideal (resp. sub modules) fulfilled ascending chain condition. We study about
Noetherian and locally Noetherian conditions for set of matrix. Some conditions that are fulfilled locally
Noetherian condition of ring and module for set of matrix are proved and also proved that Noetherian module
matrix is also Artinian module.