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

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.

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

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