A note on pseudo-injective group algebras

Abstract

A ring R is called right pseudo-injective if every R-monomorphism from a right ideal I of R to $R_R$ can be extended to an endomorphism of $R_R$. In this short note, it is proved that if K is a field with characteristic 0, then the group algebra KG is right pseudo-injective if and only if G is finite.

KEYWORDS:

• Group algebras
• pseudo-injective rings

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16S34
• 16D50

Acknowledgments

The author is grateful to the referee for carefully reading the paper and the nice suggestions.

Additional information

Funding

The research is supported by the National Natural Science Foundation of China (12071070).