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Rings which are nearly principal ideal domains

Published online by Cambridge University Press:  18 May 2009


A. W. Chatters
Affiliation:
School of Mathematics, University of Bristol, Bristol, Bs8 ITW, England, E-mail: arthurchatters@bristol.ac.uk
Corresponding

Extract

We study a class of rings which are closely related to principal ideal domains, and prove in particular that finitely-generated projective modules over such rings are free. Examples include the ring of Lipschitz quaternions; Z[a½] with d = —3 or d = —7; and any subring R of M2(Z) such that RM2(pZ) for some prime number/? and R/M2(pZ) is a field with p2 elements.


Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

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