Torsion in Mixed K-Groups

Abstract

We define generalized Milnor K-groups known as mixed K-groups and give explicit descriptions of these groups in simple cases. Our main result is a generalization of the theorem of Bass and Tate that the Milnor K-groups (k) are uniquely divisible when k is algebraically closed and n ≥ 2.

Key Words:

• Milnor K-group
• Torsion
• Divisible
• Mixed K-group

Acknowledgments

I would like to thank the National Sciences and Research Council of Canada for financial support during my years at Brown, and the Faculty Research Council of Miami University for funding my research during the summer of 2001. I am also indebted to Bruce Magurn for some stimulating conversations leading to this project.

Notes

^#Communicated by C. Pedrini.