#### Vol. 11, No. 8, 2017

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Quasi-Galois theory in symmetric monoidal categories

### Bregje Pauwels

Vol. 11 (2017), No. 8, 1891–1920
##### Abstract

Given a ring object $A$ in a symmetric monoidal category, we investigate what it means for the extension $⊮\to A$ to be (quasi-)Galois. In particular, we define splitting ring extensions and examine how they occur. Specializing to tensor-triangulated categories, we study how extension-of-scalars along a quasi-Galois ring object affects the Balmer spectrum. We define what it means for a separable ring to have constant degree, which is a necessary and sufficient condition for the existence of a quasi-Galois closure. Finally, we illustrate the above for separable rings occurring in modular representation theory.

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