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arXiv · 1911.10626

The center of the total ring of fractions

Oswaldo Lezama·Helbert Venegas
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Abstract

Let $A$ be a right Ore domain, $Z(A)$ be the center of $A$ and $Q_r(A)$ be the right total ring of fractions of $A$. If $K$ is a field and $A$ is a $K$-algebra, in this short paper we prove that if $A$ is finitely generated and ${\rm GKdim}(A)<{\rm GKdim}(Z(A))+1$, then $Z(Q_r(A))\cong Q(Z(A))$. Many examples that illustrate the theorem are included, most of them within the skew $PBW$ extensions.

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Oswaldo Lezama, Helbert Venegas. 2019-11-24. The center of the total ring of fractions. https://arxiv.org/abs/1911.10626

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