Affiliation:
1. Universitas Gadjah Mada
2. Shimane University
Abstract
Let $M=\oplus_{n\in \mathbb{Z}}M_{n}$ be a strongly graded module over strongly graded ring $D=\oplus_{n\in \mathbb{Z}} D_{n}$. In this paper, we
prove that if $M_{0}$ is a unique factorization module (UFM for short) over $D_{0}$ and $D$ is a unique factorization domain (UFD for short), then $M$ is a UFM over $D$. Furthermore, if $D_{0}$ is a Noetherian domain, we give a necessary and sufficient condition for a positively graded module $L=\oplus_{n\in \mathbb{Z}_{0}}M_{n}$ to be a UFM over positively graded domain $R=\oplus_{n\in \mathbb{Z}_{0}}D_{n}$.
Publisher
The International Electronic Journal of Algebra
Subject
Algebra and Number Theory
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