Geodesic
Representing Rank Complete Continuous Rings
Canadian journal of mathematics, Tome 28 (1976) no. 6, pp. 1320-1331

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Given a suitable regular ring R, we construct a sheaf-like representation for R as a ring of continuous sections from a completely regular space to an appropriately toplogized disjoint union of factor rings corresponding to ‘'extremal“ pseudo-rank functions. Applied to rings which are complete with respect to a rank function this representation is an isomorphism, the completely regular space is extremally disconnected and compact, and the * ‘stalks” are the simple factor rings. 
Handelman, David. Representing Rank Complete Continuous Rings. Canadian journal of mathematics, Tome 28 (1976) no. 6, pp. 1320-1331. doi: 10.4153/CJM-1976-131-9
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