Vol. 11, No. 3, 2018

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ISSN: 1944-4184 (e-only)
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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 B 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