International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 691-701
Department of Mathematics, Southeast Missouri State University, Cape Girardeau 63701, Missouri, USA
Received 28 January 1980
Copyright © 1981 Robert W. Sheets. 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 -pairs ( Henselian pairs), -pairs, and -pairs. It is shown that the 2-Henselization and the 3- Henselization of a pair exist. Characterizations of quasi-local -pairs are given, and an equivalence to the chain conjecture is proved.