A note on characterizations of rings of constants with respect to derivations

Volume 99 / 2004

Piotr Jędrzejewicz Colloquium Mathematicum 99 (2004), 51-53 MSC: Primary 12H05; Secondary 13N05. DOI: 10.4064/cm99-1-5


Let $A$ be a commutative algebra without zero divisors over a field $k$. If $A$ is finitely generated over $k$, then there exist well known characterizations of all $k$-subalgebras of $A$ which are rings of constants with respect to $k$-derivations of $A$. We show that these characterizations are not valid in the case when the algebra $A$ is not finitely generated over $k$.


  • Piotr JędrzejewiczFaculty of Mathematics and Computer Science
    N. Copernicus University
    87-100 Toruń, Poland

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