Geodesic
On the Continuity and Self-Injectivity of a Complete Regular Ring
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 404-412

Voir la notice de l'article provenant de la source Cambridge University Press

Let S be a ring, and let (ei) be an orthogonal system of a finite number of idempotents. Then e = Σei has the following properties:(i) Se Σ Sei and eS = Σ ei S.(ii) The mappings v: Se → Π Sei and w: eS → Π ei S defined by v(x) = [xei] and w(x) = [ei x] respectively are isomorphisms.Next assume that (ei)i∈I is a set of idempotents indexed by a totally ordered set I such that ei ej = 0 for every i < j. If I is finite, it is evident that has the above two properties. 
Utumi, Yuzo. On the Continuity and Self-Injectivity of a Complete Regular Ring. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 404-412. doi: 10.4153/CJM-1966-043-5
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[1] 1. Amemiya, I. and Halperin, I., Complemented modular lattices, Can. J. Math., 11 (1959), 481–520. Google Scholar

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[3] 3. Utumi, Yuzo, On continuous regular rings, Can. Math. Bull., 4 (1961), 63–69. Google Scholar

[4] 4. Utumi, Yuzo, On rings of which any one-sided quotient rings are two-sided, Proc. Amer. Math. Soc., 14 (1963), 141–147. Google Scholar

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