Geodesic
Are One-Sided Inverses Two-Sided Inverses in a Matrix Ring Over a Group Ring?
Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 475-479

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

A ring R with identity element is n-finite if for any pair A, B of n × n matrices over R, AB = In implies BA = In . In module theoretic terms, R is n-finite if and only if in a free R-module of rank n any generating set of n elements is free. If R is n-finite for all positive integers n then R is said to be strongly finite. It is known that all commutative rings, all Artinian rings and all Noetherian rings are strongly finite. These and many other interesting results appear in a paper of P. M. Cohn [1]. 
Losey, Gerald. Are One-Sided Inverses Two-Sided Inverses in a Matrix Ring Over a Group Ring?. Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 475-479. doi: 10.4153/CMB-1970-087-3
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[1] 1. Cohn, P. M., Some remarks on the invariant basis property, Topology, 5 (1966), 215-228. Google Scholar

[2] 2. Jennings, S. A., The group ring of a class of infinite nilpotent groups, Canad. J. Math. 7 (1955), 169-187. Google Scholar

[3] 3. Kaplansky, I., Rings of operators, Benjamin, New York, 1969. Google Scholar

[4] 4. Montgomery, M. S., Left and ring inverses in group algebras, Bull. Amer. Math.Soc, 75 (1969), 539-540. Google Scholar

[5] 5. Neumann, H., Varieties of Groups, Springer-Verlag, New York, 1967. Google Scholar

[6] 6. Zariski, O. and Samuel, P., Commutative Algebra, I, Van Nostrand, Princeton, 1958. Google Scholar

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