This is the first extensive treatment of the theory of corings and their comodules. In the first
part, the module-theoretic aspects of coalgebras over commutative rings are described …

Let R and S be rings, and let R ω S be a semidualizing bimodule. We prove that there exists
a Morita equivalence between the class of∞-ω-cotorsion-free modules and a subclass of the …

For any left R-module P with endomorphism ring S, the adjoint pair of functors P⊗ S− and
HomR (P,−) induce an equivalence between the categories of P-static R-modules and P …

We study the transfer of Baer-Kaplansky classes via additive functors between preadditive
categories. We show that the Baer-Kaplansky property is well behaved with respect to fully …

Generalizing the notion of Galois corings, Galois comodules were introduced as comodules
P over an A-coring 𝒞 for which PA is finitely generated and projective and the evaluation …

For an associative ring R, let P be an R-module with S= EndR (P). C. Menini and A. Orsatti
posed the question of when the related functor HomR (P,−)(with left adjoint P⊗ S−) induces …

For a long period the theory of modules over rings on the one hand and comodules and
Hopf modules for coalgebras and bialgebras on the other side developed quite …

One reason for the universal interest in Frobenius algebras is that their characterisation can
be formulated in arbitrary categories: a functor K: A→ B between categories is Frobenius if …

Tilting modules generalize projective generators and may be characterized either by
weakened generating and projectivity conditions or else by equivalences they define …

Let R and S be arbitrary rings and let CSR be a semidualizing bimodule, and let 𝒜 C⁢(R op)
and ℬ C⁢(R) be the Auslander and Bass classes, respectively. Then both pairs (𝒜 C⁢(R …