STRONG MORI MODULES OVER AN INTEGRAL DOMAIN

Title & Authors
STRONG MORI MODULES OVER AN INTEGRAL DOMAIN
Chang, Gyu Whan;

Abstract
Let D be an integral domain with quotient field K, M a torsion-free D-module, X an indeterminate, and $\small{N_v=\{f{\in}D[X]|c(f)_v=D\}}$. Let $\small{q(M)=M{\otimes}_D\;K}$ and $\small{M_{w_D}}$={$\small{x{\in}q(M)|xJ{\subseteq}M}$ for a nonzero finitely generated ideal J of D with $\small{J_v}$ = D}. In this paper, we show that $\small{M_{w_D}=M[X]_{N_v}{\cap}q(M)}$ and $\small{(M[X])_{w_{D[X]}}{\cap}q(M)[X]=M_{w_D}[X]=M[X]_{N_v}{\cap}q(M)[X]}$. Using these results, we prove that M is a strong Mori D-module if and only if M[X] is a strong Mori D[X]-module if and only if $\small{M[X]_{N_v}}$ is a Noetherian $\small{D[X]_{N_v}}$-module. This is a generalization of the fact that D is a strong Mori domain if and only if D[X] is a strong Mori domain if and only if $\small{D[X]_{N_v}}$ is a Noetherian domain.
Keywords
polynomial module;Noetherian module;strong Mori module;
Language
English
Cited by
1.
MODULES SATISFYING CERTAIN CHAIN CONDITIONS AND THEIR ENDOMORPHISMS,;;

대한수학회보, 2015. vol.52. 2, pp.549-556
1.
MODULES SATISFYING CERTAIN CHAIN CONDITIONS AND THEIR ENDOMORPHISMS, Bulletin of the Korean Mathematical Society, 2015, 52, 2, 549
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