Geodesic
Rings all of Whose Pierce Stalks are Local
Canadian mathematical bulletin, Tome 22 (1979) no. 2, pp. 159-164

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The aim of this paper is to give a number of characterizations of the rings of the title. In particular, these turn out to be precisely those exchange rings whose idempotents are all central. They are also those rings in which every element is the sum of a unit and a central idempotent. 
Burgess, W. D.; Stephenson, W. Rings all of Whose Pierce Stalks are Local. Canadian mathematical bulletin, Tome 22 (1979) no. 2, pp. 159-164. doi: 10.4153/CMB-1979-022-8
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