Rings which are nearly principal ideal domains

Rings which are nearly principal ideal domains

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 R ⊇ M2(pZ...

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Veröffentlicht in:Glasgow mathematical journal 1998-09, Vol.40 (3), p.343-351
1. Verfasser: Chatters, A. W.
Format: Artikel
Sprache:eng
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Zusammenfassung: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 R ⊇ M2(pZ) for some prime number/? and R/M2(pZ) is a field with p2 elements.
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089500032699