Goldie Extending Rings

Abstract

In this article, we investigate the 𝒢-extending condition under various ring extensions. We show that if R _R is 𝒢-extending and S is a right essential overring, then S _R and S _S are 𝒢-extending. For split-null extensions, we show that if M ⊴ R and M is left faithful, then R _R is (𝒢-) extending if and only if S _S is (𝒢-) extending, where S = S(R, M). This result appears to be new for the extending case. We conclude with results on Dorroh extensions.

Key Words:

• Essential overring
• Extending module
• Goldie extending module
• Split-null extension

2000 Mathematics Subject Classification:

• Primary 16D70, 16D50
• Secondary 16D80

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Corrigendum

ACKNOWLEDGMENTS

This work was made possible by TUBITAK (BIDEP) and was carried out during visits of the second author to Hacettepe University. The authors wish to thank both organizations for their support. The second author is grateful for the hospitality shown to him by the faculty and staff of Hacettepe University.

Notes

Communicated by T. Albu.