# Positive characteristic analogs of closed polynomials

Open Mathematics (2011)

- Volume: 9, Issue: 1, page 50-56
- ISSN: 2391-5455

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topPiotr Jędrzejewicz. "Positive characteristic analogs of closed polynomials." Open Mathematics 9.1 (2011): 50-56. <http://eudml.org/doc/269507>.

@article{PiotrJędrzejewicz2011,

abstract = {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.},

author = {Piotr Jędrzejewicz},

journal = {Open Mathematics},

keywords = {Closed polynomial; Derivation; Ring of constants; closed polynomial; derivations; rings of constants},

language = {eng},

number = {1},

pages = {50-56},

title = {Positive characteristic analogs of closed polynomials},

url = {http://eudml.org/doc/269507},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Piotr Jędrzejewicz

TI - Positive characteristic analogs of closed polynomials

JO - Open Mathematics

PY - 2011

VL - 9

IS - 1

SP - 50

EP - 56

AB - 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.

LA - eng

KW - Closed polynomial; Derivation; Ring of constants; closed polynomial; derivations; rings of constants

UR - http://eudml.org/doc/269507

ER -

## References

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- [5] Jędrzejewicz P., One-element p-bases of rings of constants of derivations, Osaka J. Math., 2009, 46(1), 223–234 Zbl1159.13014
- [6] Nowicki A., On the jacobian equation J(f, g) = 0 for polynomials in k[x, y], Nagoya Math. J., 1988, 109, 151–157 Zbl0642.13016
- [7] Nowicki A., Polynomial Derivations and their Rings of Constants, UMK, Toruń, 1994 Zbl1236.13023
- [8] Nowicki A., Nagata M., Rings of constants for k-derivations in k[x 1, ..., x n], J. Math. Kyoto Univ., 1988, 28(1), 111–118 Zbl0665.12024
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- [10] Schinzel A., Polynomials with Special Regard to Reducibility, Encyclopedia Math. Appl., 77, Cambridge University Press, Cambridge, 2000

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