Positive characteristic analogs of closed polynomials

• Autorzy: Piotr Jędrzejewicz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Closed polynomial; Derivation; Ring of constants

Kategorie tematyczne

• 12E05: Polynomials (irreducibility, etc.)
• 13N15: Derivations
• 13B22: Integral closure of rings and ideals ; integrally closed rings, related rings (Japanese, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 1
• Strony: 50-56

Daty

wydano

2011-02-01

online

2010-12-30

Twórcy

autor

Piotr Jędrzejewicz

• Nicolaus Copernicus University,

Bibliografia

• [1] Arzhantsev I.V., Petravchuk A.P., Closed polynomials and saturated subalgebras of polynomial algebras, Ukrainian Math. J., 2007, 59(12), 1783–1790 http://dx.doi.org/10.1007/s11253-008-0037-4
• [2] Ayad M., Sur les polynômes f(X, Y) tels que K[f] est intégralement fermé dans K[X, Y], Acta Arith., 2002, 105(1), 9–28 http://dx.doi.org/10.4064/aa105-1-2
• [3] Jędrzejewicz P., Rings of constants of p-homogeneous polynomial derivations, Comm. Algebra, 2003, 31(11), 5501–5511 http://dx.doi.org/10.1081/AGB-120023970
• [4] Jędrzejewicz P., Eigenvector p-bases of rings of constants of derivations, Comm. Algebra, 2008, 36(4), 1500–1508 http://dx.doi.org/10.1080/00927870701869014
• [5] Jędrzejewicz P., One-element p-bases of rings of constants of derivations, Osaka J. Math., 2009, 46(1), 223–234
• [6] Nowicki A., On the jacobian equation J(f, g) = 0 for polynomials in k[x, y], Nagoya Math. J., 1988, 109, 151–157
• [7] Nowicki A., Polynomial Derivations and their Rings of Constants, UMK, Toruń, 1994
• [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
• [9] Płoski A., On the irreducibility of polynomials in several complex variables, Bull. Polish Acad. Sci. Math., 1991, 39(3–4), 241–247
• [10] Schinzel A., Polynomials with Special Regard to Reducibility, Encyclopedia Math. Appl., 77, Cambridge University Press, Cambridge, 2000

Identyfikatory

DOI

10.2478/s11533-010-0091-7