# On the algebra of constants of polynomial derivations in two variables

Colloquium Mathematicae (2000)

- Volume: 83, Issue: 2, page 267-269
- ISSN: 0010-1354

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topZieliński, Janusz. "On the algebra of constants of polynomial derivations in two variables." Colloquium Mathematicae 83.2 (2000): 267-269. <http://eudml.org/doc/210785>.

@article{Zieliński2000,

abstract = {Let d be a k-derivation of k[x,y], where k is a field of characteristic zero. Denote by $\widetilde\{d\}$ the unique extension of d to k(x,y). We prove that if ker d ≠ k, then ker $\widetilde\{d\}$ = (ker d)0, where (ker d)0 is the field of fractions of ker d.},

author = {Zieliński, Janusz},

journal = {Colloquium Mathematicae},

language = {eng},

number = {2},

pages = {267-269},

title = {On the algebra of constants of polynomial derivations in two variables},

url = {http://eudml.org/doc/210785},

volume = {83},

year = {2000},

}

TY - JOUR

AU - Zieliński, Janusz

TI - On the algebra of constants of polynomial derivations in two variables

JO - Colloquium Mathematicae

PY - 2000

VL - 83

IS - 2

SP - 267

EP - 269

AB - Let d be a k-derivation of k[x,y], where k is a field of characteristic zero. Denote by $\widetilde{d}$ the unique extension of d to k(x,y). We prove that if ker d ≠ k, then ker $\widetilde{d}$ = (ker d)0, where (ker d)0 is the field of fractions of ker d.

LA - eng

UR - http://eudml.org/doc/210785

ER -

## References

top- [1] A. Nowicki, Polynomial Derivations and Their Rings of Constants, N. Copernicus University Press, Toruń, 1994. Zbl1236.13023
- [2] S. Sato, On the ring of constants of a derivation of ℝ[x,y], Rep. Fac. Engrg. Oita Univ. 39 (1999), 13-16.

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