Abstract
The historical development of Hensel's lemma is briefly discussed ( Section 1). Using Newton polygons, a simple proof of a general Hensel's lemma for separable polynomials over Henselian fields is given ( Section 3). For polynomials over algebraically closed, valued fields, best possible results on continuity of roots ( Section 4) and continuity of factors ( Section 6) are demonstrated. Using this and a general Krasner's lemma ( Section 7), we give a short proof of a general Hensel's lemma and show that it is, in a certain sense, best possible ( Section 8). All valuations here are non-Archimedean and of arbitrary rank. The article is practically self-contained.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
