Geodesic
Completions of Rank Rings
Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 199-205

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In this note, we prove three results on regular rings possessing a rank function: (a) the completion of a *-regular rank ring is a regular Baer *-ring; (b) (a) is used to construct regular Baer * factors of type IIf with centre any complex subfield closed under conjugation; (c) the units of a unit-regular rank ring form a dense topological subgroup of the units of the completion. 
Handelman, David. Completions of Rank Rings. Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 199-205. doi: 10.4153/CMB-1977-032-3
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