The notion of a closed polynomial over a field of zero characteristic was introduced by Nowicki and Nagata. In this paper we discuss possible ways to define an analog of this notion over fields of positive characteristic. We are mostly interested in conditions of maximality of the algebra generated by a polynomial in a respective family of rings. We also present a modification of the condition of integral closure and discuss a condition involving partial derivatives.
@article{bwmeta1.element.doi-10_2478_s11533-010-0091-7,
author = {Piotr J\k edrzejewicz},
title = {Positive characteristic analogs of closed polynomials},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {50-56},
zbl = {1211.12005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0091-7}
}
Piotr Jędrzejewicz. Positive characteristic analogs of closed polynomials. Open Mathematics, Tome 9 (2011) pp. 50-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0091-7/
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