Proceedings of the Japan Academy, Series A, Mathematical Sciences

Certain rings whose simple singular modules are GP-injective

Jin Yong Kim

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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.

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

First available in Project Euclid: 3 October 2005

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Zentralblatt MATH identifier

Primary: 16D50: Injective modules, self-injective rings [See also 16L60] 16E50: von Neumann regular rings and generalizations

Generalized principally injective module idempotent reflexive ring simple singular module von Neumann regular ring Goldie ring


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.

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