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Bicontinuous Isomorphisms between Two Closed Left Ideals of a Compact Dual Ring

Published online by Cambridge University Press:  20 November 2018

Ling-Erl E. T. Wu
Ling-Erl E. T. Wu*
Affiliation:
Cowell College, University of Californiaat Santa Cruz
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1148 - 1151
Copyright
Copyright © Canadian Mathematical Society 1966

References

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