STRONGLY GRADED RINGS WHICH ARE KRULL RINGS
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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- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI