## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Certain rings whose simple singular modules are GP-injective

Jin Yong Kim

#### Abstract

We prove that if $R$ is an idempotent reflexive left Goldie ring whose simple singular left $R$-modules are GP-injective, then $R$ is a finite product of simple left Goldie rings. As a byproduct of this result we are able to show that if $R$ is semiprime, left Goldie and left weakly $\pi$-regular, then $R$ is a finite product of simple left Goldie rings.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 7 (2005), 125-128.

Dates
First available in Project Euclid: 3 October 2005

https://projecteuclid.org/euclid.pja/1128346015

Digital Object Identifier
doi:10.3792/pjaa.81.125

Mathematical Reviews number (MathSciNet)
MR2172601

Zentralblatt MATH identifier
1089.16004

#### Citation

Kim, Jin Yong. Certain rings whose simple singular modules are GP -injective. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 7, 125--128. doi:10.3792/pjaa.81.125. https://projecteuclid.org/euclid.pja/1128346015

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