Geodesic
Bicontinuous Isomorphisms between Two Closed Left Ideals of a Compact Dual Ring
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1148-1151

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A quasi-Frobenius ring is a ring with minimum condition satisfying the conditions r(l)H)) = H and l(r(L)) = L for right ideals H and left ideals L where r(S) (l(S)) denotes the right (left) annihilator of a subset S of the ring. Nakayama first defined and studied such rings (8; 9) and they have been studied by a number of authors (2; 3; 4; 6). A dual ring is a topological ring satisfying the conditions r(l)H)) = H and l(r)H)) = L for closed right ideals H and closed left ideals L. Baer (1) and Kaplansky (7) introduced the notion of such rings, which is a natural generalization of that of quaso-Frobenius rings. Numakura studied the analogy between dual rings and quasi-Frobenius rings in (10). 
Wu, Ling-Erl E. T. Bicontinuous Isomorphisms between Two Closed Left Ideals of a Compact Dual Ring. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1148-1151. doi: 10.4153/CJM-1966-114-4
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