Centralizers in Domains of Finite Gelfand-Kirillov Dimension

Details Centralizers in Domains of Finite Gelfand-Kirillov Dimension Centralizers in Domains of Finite Gelfand-Kirillov Dimension

2008-10-17

arxiv.org/abs/0810.3054v1

Mathematics

Rings and Algebras

4 pages

Scientific paper

We study centralizers of elements in domains. We generalize a result of the author and Small, showing that if $A$ is a finitely generated noetherian domain and $a\in A$ is not algebraic over the extended centre of $A$, then the centralizer of $a$ has Gelfand-Kirillov dimension at most one less than the Gelfand-Kirillov dimension of $A$. In the case that $A$ is a finitely generated noetherian domain of GK dimension 3 over the complex numbers, we show that the centralizer of an element a $A$ that is not algebraic over the extended centre of $A$ satisfies a polynomial identity.

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