فهرست نشریات علمی دسترسی آزاد ایران

In this paper we shall introduce a theory of length for Artinian modules over an arbitrary ring (with identity), assigning to each Artinian module $A$ an ordinal number $len(A)$ which will briefly be called the length of $A$. We also demonstrate for some familiar properties of left Artinian ring be proved efficiently using length and arithmetic properties of ordinal numbers.