Conference abstracts

Session S05 - Rings and Algebras

July 29, 17:30 ~ 17:55

On $D$ algebras.

Leonid Makar-Limanov

Wayne State University, USA   -

Consider an algebraic function $z$ of $n$ variables $x_1, x_2, \dots, x_n$. Denote by $D(z)$ a subalgebra of the field ${\Bbb C}(x_1, x_2, \dots, x_n)[z]$ which is generated by $x_1, x_2, \dots, x_n; \ z$ and all partial derivatives of $z$. I am interested in properties of algebras $D(z)$.

In my talk I will discuss the following conjectural dichotomy:

If $z \in {\Bbb C}[x_1, \dots, x_n]$ then (obviously) $D(z) = {\Bbb C}[x_1, \dots, x_n]$, but if $z \not\in {\Bbb C}[x_1, \dots, x_n]$ then $D(z)$ cannot be embedded into a polynomial ring.

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