STRONGLY GRADED RINGS WHICH ARE KRULL RINGS

Year 2019, Volume: 25 Issue: 25, 120 - 128, 08.01.2019

İndah Emilia Wijayanti Hidetoshi Marubayashi İwan Ernanto Akira Ueda

https://doi.org/10.24330/ieja.504135

Cited By: 1

https://izlik.org/JA83RD53RU

Abstract

Let $R = \oplus_{n \in \Z} R_{n}$ be a strongly graded ring of type $\Z$ and $R_{0}$ is a prime Goldie ring. It is shown that the following three conditions are equivalent: (i) $R_{0}$ is a $\Z$-invariant Krull ring, (ii) $R$ is a Krull ring and (iii) $R$ is a graded Krull ring. We completely describe all $v$-invertible $R$-ideals in $Q$, where $Q$ is a quotient ring of $R$.

 

Keywords

Strongly graded ring , prime Goldie ring , Krull ring , v-invertible R-ideal

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