Yazd University Algebraic Structures and Their Applications 2382-9761 10 1 2023 02 01 A length for Artinian modules 151 164 2917 10.22034/as.2022.2917 EN Alireza Alehafttan Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran. Journal Article 2022 06 18 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. Artinian module Length dimension Length function Length rank Strictly increasing function https://as.yazd.ac.ir/article_2917_065e5a098607aa7a1b9ad99fe4b5baba.pdf