A note on the first nonzero Fitting ideal of a module

Document Type : Research Paper

Author

Department of Mathematics, Vali-e-Asr University of Rafsanjan, Iran

10.48308/cgasa.2025.236826.1518

Abstract

Let $R$ be a commutative  ring and $M$ be a finitely generated $R$-module.   Let   I$(M)$ be the first nonzero Fitting ideal of $M$.  In this paper we characterize some modules over Noetherian UFDs, whose first nonzero Fitting ideal is a prime ideal. We show that if $P$ is a prime ideal and $M$ is a finitely generated R-module with I$(M) = P$ and T$(M_P)\neq 0$, then M is isomorphic to $R/P \oplus N$, for some projective R-module $N$ of constant rank. Also,  we investigate some conditions under which  ${M}/$T$(M)$ is free.

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