Stable equivalence of Morita type and Frobenius extensions
Abstract
A.S. Dugas and R. Martínez-Villa proved in \cite[Corollary 5.1]{dm} that if there exists a stable equivalence of Morita type between the
k
-algebras
Λ
and
Γ
, then it is possible to replace
Λ
by a Morita equivalent
k
-algebra
Δ
such that
Γ
is a subring of
Δ
and the induction and restriction functors induce inverse stable equivalences. In this note we give an affirmative answer to a question of Alex Dugas about the existence of a
Γ
-coring structure on
Δ
. We do this by showing that
Δ
is a Frobenius extension of
Γ
.