Morita equivalence of rings has been studied extensively. However, it seems that Morita equivalence in
ring extensions is not well known.
In 1970, Y. Miyashita introduced the notion of Morita equivalence in ring extensions. It has already been
proved that some classes of well-known ring extensions (separable extensions, Hirata separable
extensions, G-Galois extensions, Frobenius extensions, symmetric extensions, and GF-extensions) are
Morita invariant by Y. Miyashita and S. Ikehata.
In this talk, we shall characterize Morita equivalence in ring extensions in terms of categorical properties
and we shall prove that several classes of ring extensions are Morita invariant.