On the order of a module

Document Type : Research Paper


Department of‎ ‎Mathematics‎, ‎Vali-e-Asr University of Rafsanjan‎, ‎P.O‎. ‎Box 7718897111‎, ‎Rafsanjan‎, ‎Iran.


Abstract. Let $(R,P)$ be a Noetherian unique factorization domain (UFD) and M be a finitely generated R-module. Let I(M)
be the first nonzero Fitting ideal of M and the order of M, denoted $ord_R(M)$, be the largest integer n such that $I(M) ⊆ P^n$. In this paper, we show that if M is a module of order one, then either M is isomorphic with direct sum of a free module and a cyclic module or M is isomorphic with a special module represented in the text. We also assert some properties of M while $ord_R(M) = 2.$


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