Geodesic
Orthogonally Complete Rings
Canadian mathematical bulletin, Tome 20 (1977) no. 3, pp. 347-351

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In this note we continue the study of Abian's order for reduced rings initiated in papers such as [1], [5], [3], [4]. A simple proof is given of Abian's result that taking suprema commutes with ring multiplication. The properties of orthogonally complete rings and of rings satisfying chain conditions with respect to Abian's order are investigated. 
Raphael, R.; Stephenson, W. Orthogonally Complete Rings. Canadian mathematical bulletin, Tome 20 (1977) no. 3, pp. 347-351. doi: 10.4153/CMB-1977-052-6
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     author = {Raphael, R. and Stephenson, W.},
     title = {Orthogonally {Complete} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {347--351},
     year = {1977},
     volume = {20},
     number = {3},
     doi = {10.4153/CMB-1977-052-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-052-6/}
}
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