#### Vol. 11, No. 3, 2018

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Nested Frobenius extensions of graded superrings

### Edward Poon and Alistair Savage

Vol. 11 (2018), No. 3, 449–461
##### Abstract

We prove a nesting phenomenon for twisted Frobenius extensions. Namely, suppose $R\subseteq B\subseteq A$ are graded superrings such that $A$ and $B$ are both twisted Frobenius extensions of $R$, $R$ is contained in the center of $A$, and $A$ is projective over $B$. Our main result is that, under these assumptions, $A$ is a twisted Frobenius extension of $B$. This generalizes a result of Pike and the second author, which considered the case where $R$ is a field.

##### Keywords
Frobenius extension, Frobenius algebra, graded superring, graded superalgebra
##### Mathematical Subject Classification 2010
Primary: 17A70, 16W50
##### Milestones
Received: 5 May 2016
Revised: 27 June 2017
Accepted: 28 June 2017
Published: 20 October 2017

Communicated by Kenneth S. Berenhaut
##### Authors
 Edward Poon Department of Mathematics and Statistics University of Ottawa Ottawa Canada Alistair Savage Department of Mathematics and Statistics University of Ottawa Ottawa Canada