Conference abstracts

Session S05 - Rings and Algebras

July 28, 18:30 ~ 18:55

## Automorphisms of ideals of polynomial rings

### Thiago Castilho de Mello

### Universidade Federal de São Paulo, Brasil - castilho.thiago@gmail.com

Let $R$ be a commutative integral domain with unit, $f$ be a nonconstant monic polynomial in $R[t]$, and $I_f \subset R[t]$ be the ideal generated by $f$. Such ideal may be considered as an $R$-algebra. In this talk we present recent results obtained with T. Macedo [arXiv:1604.08531], concerning the group $Aut(I_f)$, of $R$-algebra automorphisms of $I_f$. We will show that $Aut(I_f)$ can be obtained by analyzing some symmetries of the roots of $f$ in the algebraic closure of the quotient field of $R$ (counted with multiplicities). In particular, we show that, under certain mild hypothesis, if $f$ has at least two different roots in the algebraic closure of the quotient field of $R$, then $Aut(I_f)$ is a cyclic group and its order can be completely determined by analyzing the roots of $f$.

Supported by Fapesp and CNPq

Joint work with Tiago Macedo (Universidade Federal de São Paulo).