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.
Hadjirezaei, S. (2025). A note on the first nonzero Fitting ideal of a module. Categories and General Algebraic Structures with Applications, (), -. doi: 10.48308/cgasa.2025.236826.1518
MLA
Hadjirezaei, S. . "A note on the first nonzero Fitting ideal of a module", Categories and General Algebraic Structures with Applications, , , 2025, -. doi: 10.48308/cgasa.2025.236826.1518
HARVARD
Hadjirezaei, S. (2025). 'A note on the first nonzero Fitting ideal of a module', Categories and General Algebraic Structures with Applications, (), pp. -. doi: 10.48308/cgasa.2025.236826.1518
CHICAGO
S. Hadjirezaei, "A note on the first nonzero Fitting ideal of a module," Categories and General Algebraic Structures with Applications, (2025): -, doi: 10.48308/cgasa.2025.236826.1518
VANCOUVER
Hadjirezaei, S. A note on the first nonzero Fitting ideal of a module. Categories and General Algebraic Structures with Applications, 2025; (): -. doi: 10.48308/cgasa.2025.236826.1518
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