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The Eleventh Summer Conference on General Topology and Applications
August 10-13, 1995
University of Southern Maine
Gorham, ME, USA

Organizers
J. Baumgartner, D. Briggs, J. deBakker, B. Flagg, G. Gruenhage, M. Guay, Y. Kong, R. Kopperman, S. Shore, J. Rutten, J. Vaughan

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Topological rings with linearly compact open subrings
by
M. Ursul
Institutul de matematica, Republica Moldova

A topological ring is called hereditarily linearly compact if each of its closed subrings is linearly compact.

We study the relation between hereditarily linearly compact rings and topological rings, all of whose open subrings are linearly compact.

Theorem 1. Let R be a topological ring having a fundamental system of neighborhoods of zero of two-sided ideals. If every open subring of R is linearly compact, then R is hereditarily linearly compact.

Theorem 2. Let F be a finite field and V an infinite left verctor F-space. Then every open subring of End(V) is linearly compact, but End(V) is not hereditarily linearly compact.

Date received: April 12, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaf-87.