STRONGLY GRADED RINGS WHICH ARE KRULL RINGS

Authors : İndah Emilia WİJAYANTİ, Hidetoshi MARUBAYASHİ, İwan ERNANTO, Akira UEDA

Pages : 120-128

Doi:10.24330/ieja.504135

View : 24 | Download : 12

Publication Date : 2019-01-08

Article Type : Research Paper

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: insert ignore into journalissuearticles values(i); $R_{0}$ is a $\Z$-invariant Krull ring, insert ignore into journalissuearticles values(ii); $R$ is a Krull ring and insert ignore into journalissuearticles values(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