ABELIAN EXCHANGE MODULES

ABSTRACT

Let M_k be a right k-module with endomorphism ring E=End(M_k). We prove that if E is an Abelian exchange ring, then M_k has the full exchange property. We also give an extension of this result in the case E is regular.

Key Words:

• Abelian ring
• Exchange property

Mathematics Subject Classification:

• 16D70
• 16P99

ACKNOWLEDGMENTS

My thanks to my advisor T. Y. Lam for introducing me to this subject and carefully reading manuscripts and giving suggestions. Also a warm thanks to the referee, whose comments led to a substantial improvement in the manuscript.

Notes

^#Communicated by J. L. Gomez Pardo.