PRIMENESS IN MODULES AND SOME ZERO DIMENSIONAL RINGS

Let R be a commutative ring with 1 6= 0 and M be a unitary R-module. Let S(M) is the set of submodules of M and Á : S(M) ¡! S(M) [ f;g be a function. Suppose n ¸ 2 is a positive integer. In this paper we define (n ¡ 1; n) ¡ Á-prime submodules (n ¸ 2). A number of results concerning (n¡1; n)¡Á-prime submodules are given.Also we study some zero dimensional rings