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A Remark on a Paper of Crachiola and Makar-Limanov

Dryło R.

Bulletin of the Polish Academy of Sciences. Mathematics

2011

Vol. 59, no 3

203--206

A. Crachiola and L. Makar-Limanov [J. Algebra 284 (2005)] showed the following: if X is an affine curve which is not isomorphic to the affine line A1k, then ML(X×Y)=k[X]⊗ML(Y) for every affine variety Y, where k is an algebraically closed field. In this note we give a simple geometric proof of a more general fact that this property holds for every affine variety X whose set of regular points is not k-uniruled.