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

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

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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[1] 1. Abian, A., Direct product decomposition of commutative semi-simple rings, Proc. Amer. Math. Soc. 24 (1970), 502-507. Google Scholar

[2] 2. Armendariz, E. P., A note on extensions of Baer and p.p.-rings, J. Austral. Math. Soc. 18 (1974), 470-473. Google Scholar

[3] 3. Burgess, W. D. and Raphael, R., Abian's order relation and orthogonal completeness for reduced rings, Pac. J. Math. 54 (1974), 55-64. Google Scholar

[4] 4. Burgess, W. D. and Raphael, R., Complete and orthogonally complete rings, Can. Jour. Math. 27 (1975), (to appear). Google Scholar

[5] 5. Chacron, M., Direct products of division rings and a paper of Abian. Proc. Amer. Math. Soc. 29 (1971), 259-262. Google Scholar

[6] 6. Gilmer, R. W., Power series rings over a Krull domain, Pac. Jour. Math. 29 (1969), 543-549. Google Scholar

[7] 7. Lambek, J., Lectures on rings and modules, Waltham, Massachusetts, Ginn, 1966. Google Scholar

[8] 8. Speed, T., A Note On Commutative Baer Rings, J. Australian, Math. Soc. 14 (1972), 257-263. Google Scholar

[9] 9. Utumi, Y., On continuous regular rings and semi-simple self-injective rings, Can. J. Math. 12 (1960), 597-605. Google Scholar

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