The composition of dualities in a nondegenerate Morita context

Morita contexts and unitary ideals of rings

“…Then Id([Γ • Γ]) = (Φ, Θ), where Remark. Note that if we do not consider sub-bimodules as in Theorem 3.7, but only one-sided submodules, then a Morita context (R, S, R P S , S Q R , θ , φ ) induces in a natural way certain contravariant Galois connections between the lattices of left ideals of S, right ideals of S, submodules of R P and submodules of Q R (see [9]).…”

Morita Contexts and their Lattices of Relations

“…The presented results were inspired by a similar situation for Morita contexts between rings (see Kashu, 1998).…”

“…Section 2 is devoted to show how the dualities and projectivities are related. Section 3 shortly translates the results of Section 2 into the setting of the lattice of all subacts (submodules as in Kashu (1998)). …”