Geodesic
Rings which are nearly principal ideal domains
Glasgow mathematical journal, Tome 40 (1998) no. 3, pp. 343-351

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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[a1⁄2] 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. 
Chatters, A. W. Rings which are nearly principal ideal domains. Glasgow mathematical journal, Tome 40 (1998) no. 3, pp. 343-351. doi: 10.1017/S0017089500032699
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