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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Maximal and minimal ring topologies


Author: Niel Shell
Journal: Proc. Amer. Math. Soc. 68 (1978), 23-26
MSC: Primary 12J99
DOI: https://doi.org/10.1090/S0002-9939-1978-0460305-3
MathSciNet review: 0460305
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Abstract: An explicit description is given of a nondiscrete ring topology on the field Q of rational numbers which is strictly finer than the locally bounded topology on Q having the ring of integers as a preorder. It is observed that either there exist nonvaluable minimal ring topologies or there exist ring topologies containing no minimal ring topologies.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0460305-3
Keywords: Field topology, non-Archimedean ring topology, non-Archimedean uniformity, minimal ring topology, maximal ring topology, nonideal topology, sigma-bounded ring topology, lattice of ring topologies
Article copyright: © Copyright 1978 American Mathematical Society