Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Positive characteristic analogs of closed polynomials

100%

Jędrzejewicz P.

Open Mathematics

2011

tom 9

nr 1

50-56

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.

One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal

100%

Lierde V.

Open Mathematics

2011

tom 9

nr 6

1349-1353

Let (R;m) be a 2-dimensional rational singularity with algebraically closed residue field and whose associated graded ring is an integrally closed domain. Göhner has shown that for every prime divisor v of R, there exists a unique one-fibered complete m-primary ideal A v in R with unique Rees valuation v and such that any complete m-primary ideal with unique Rees valuation v, is a power of A v. We show that for v ≠ ordR, A v is the inverse transform of a simple complete ideal in an immediate quadratic transform of R, if and only if the degree coefficient d(A v; v) is 1. We then give a criterion for R to be regular.

Ograniczanie wyników

2 Open Mathematics

1 Jędrzejewicz P.

1 Lierde V.

2 2011

Wyniki wyszukiwania

Positive characteristic analogs of closed polynomials

One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal