School of Mathematics Seminars and Lectures
`On splitting of primes and simple extensions of integrally closed domains'
by Prof. S.K. Khanduja (IISER, Mohali)
Thursday, November 27, 2014
from
to
(Asia/Kolkata)
at AG-77
at AG-77
Description |
We will discuss an extension of the classical Dedekind's theorem regarding splitting of rational primes in algebraic number fields as well as of its converse when the base field is a valued field of arbitrary rank. Let $R$ be the valuation ring of a Krull valuation defined on a field $K$ and $S$ be the integral closure of $R$ in a finite extension $L$ of $K.$ A set of conditions will be described which are necessary as well as sufficient for $S$ to be a simple ring extension of $R,$ i.e., $S=R[\theta]$ for some $\theta.$ The well known theorem of Dedekind characterizing those rational primes $p$ which divide the index of an algebraic number field will be deduced. Some related open problems will also be mentioned. |