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International Journal of Mathematics and Mathematical Sciences
Volume 4, Issue 4, Pages 691-701

Partial henselizations

Department of Mathematics, Southeast Missouri State University, Cape Girardeau 63701, Missouri, USA

Received 28 January 1980

Copyright © 1981 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We define and note some properties of kH-pairs (k Henselian pairs), kN-pairs, and kN-pairs. It is shown that the 2-Henselization and the 3- Henselization of a pair exist. Characterizations of quasi-local 2H-pairs are given, and an equivalence to the chain conjecture is proved.