Geodesic
A Remark on a Paper of Crachiola and Makar-Limanov
Robert Dryło1
1 Instytut Matematyczny PAN Śniadeckich 8 00-956 Warszawa, Poland and Instytut Matematyki Uniwersytet Jana Kochanowskiego w Kielcach Świętokrzyska 15 25-406 Kielce, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 3, pp. 203-206.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\mathbb A^1_k$, then $\mathop{\rm ML}(X\times Y)=k[X]\otimes \mathop{\rm ML}(Y)$ 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.
DOI : 10.4064/ba59-3-2
Keywords: crachiola makar limanov algebra showed following affine curve which isomorphic affine line mathbb mathop times otimes mathop every affine variety where algebraically closed field note simple geometric proof general property holds every affine variety whose set regular points k uniruled

Robert Dryło 1

1 Instytut Matematyczny PAN Śniadeckich 8 00-956 Warszawa, Poland and Instytut Matematyki Uniwersytet Jana Kochanowskiego w Kielcach Świętokrzyska 15 25-406 Kielce, Poland 
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Robert Dryło. A Remark on a Paper of Crachiola and Makar-Limanov. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 3, pp. 203-206. doi : 10.4064/ba59-3-2. http://geodesic.mathdoc.fr/articles/10.4064/ba59-3-2/

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