Reflexive Modules over Coherent GCD-Domains

ABSTRACT

In this article, we study finitely generated reflexive modules over coherent GCD-domains and finitely generated projective modules over polynomial rings. In particular, we give a sufficient condition for a finitely generated reflexive module over a coherent GCD-domain to be a free module. By use of this result, we prove that every finitely generated projective R + [X]-module can be extended from R if R is a commutative ring with gl.dim(R) ≤ 2.

ACKNOWLEDGMENTS

The authors would like to thank the referee for several helpful comments, and is supported by the National Natural Science Foundation of China(10271052), Guangxi Natural Science Foundation(0221029), the Support Program for 100 Young and Middle-Aged Discipliary Leaders in Guangxi Higher Education Institutions and Scientific Research Foundation of Guangxi Educational Committee.

Notes

^#Communicated by S. Goto.