regular divisors of a submodule

In this article, we extend the concept of divisors to ideals of noetherian rings, more generally, to submodules of finitely generated modules over noetherian rings. for a submodule n of a finitely generated module m over a noetherian ring, we say a submodule k of m is a regular divisor of n in m if k occurs in a regular prime extension filtration of m over n. we show that a submodule n of m has only a finite number of regular divisors in m. we also show that an ideal b is a regular divisor of a non-zero ideal a in a dedekind domain r if and only if b contains a. we characterize regular divisors using some ordered sequences of prime ideals and study their various properties. lastly, we formulate a method to compute the number of regular divisors of a submodule by solving a combinatorics problem.