On Fully (m,n)-stable modules relative to an ideal A of R n×m

Let R be a commutative ring with non-zero identity element. For two fixed positive integers m and n. A right R-module M is called fully (m,n) -stable relative to ideal A of n m R n×m , if 0 (N) ≤ N+ Mn A for each n-generated submodule of Mm and Rhomomorphism 0:N -Mm .In this paper we give some characterization theorems and properties of fully (m,n) -stable modules relative to an ideal A of n m R n×m . which generalize the results of fully stable modules relative to an ideal A of R. Key words: fully (m,n) -stable modules relative to an ideal A of n m Rn×m ,(m,n)- multiplication modules and (m,n)-quasi injective modules.