A length for Artinian modules

Document Type : Research Paper

Author

Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran.

Abstract

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.

Keywords


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