Nested Frobenius extensions of graded superrings

Poon, Edward; Savage, Alistair

doi:10.2140/involve.2018.11.449

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Nested Frobenius extensions of graded superrings

Edward Poon and Alistair Savage

Vol. 11 (2018), No. 3, 449–461

DOI: 10.2140/involve.2018.11.449

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

Vol. 11, No. 3, 2018