On Maximal Subalgebras

Abstract

Let $\text{k}$ be an algebraically closed field. We classify all maximal $\text{k}$-subalgebras of any one-dimensional finitely generated $\text{k}$-domain. In dimension two, we classify all maximal $\text{k}$-subalgebras of $\text{k}[t,t^{-1},y]$. To the authors' knowledge, this is the first such classification result for an algebra of dimension $>1$. In the course of this study, we classify also all maximal $\text{k}$-subalgebras of $\text{k}[t,y]$ that contain a coordinate. Furthermore, we give examples of maximal $\text{k}$-subalgebras of $\text{k}[t,y]$ that do not contain a coordinate.

30 pages, typos corrected, minor changes, improved exposition

Cited by in corpus (1)

• Conch Maximal Subrings