IJPAM: Volume 103, No. 2 (2015)

EPIMORPHISM OF RINGS AND
ABSOLUTELY FLAT MODULES

S. Mangayarcarassy
Department of Mathematics
Pondicherry Engineering College
Pondicherry, 605014, INDIA


Abstract. Let $ R \subset S $ be a commutative ring extension. We prove that if $ \phi : R \to S $ is an epimorphism of rings with $ \phi $ injective homomorphism and $ S $ is $R$-projective, then an $R$-module $ M $ is $R$-injective and $ S $ is absolutely flat over $R$ if and only if $ \hmo_R(S,M) $ is $ S $-injective and $ S $ is an absolutely flat ring.

Received: January 22, 2015

AMS Subject Classification: 13C11, 13D07, 13E05

Key Words and Phrases: projective modules, injective modules, epimorphism of rings, absolutely flat modules

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DOI: 10.12732/ijpam.v103i2.3 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 103
Issue: 2
Pages: 163 - 168


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