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Orthogonally complete rings

1977
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Canadian mathematical bulletin
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Introduction. 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. Finally those rings JR for which R[x] and JR [[x]] are orthogonally complete are characterized. These results provide interesting

doi:10.4153/cmb-1977-052-6
fatcat:2su3nmkpu5fwnjnqxd4npv5mpa