We introduce partial (co) actions of a Hopf algebra H on an algebra. To this end, we
introduce first the notion of lax coring, generalizing Wisbauer's notion of weak coring. We …

EXPOSITORY PAPER Partial actions: what they are and why we care Page 1 EXPOSITORY
PAPER Partial actions: what they are and why we care Eliezer Batista Abstract We present a …

We study the corings whose category of right comodules has a finitely generated projective
generator. In order to extricate the structure of these corings, we introduce the notion of …

We develop Hopf-Galois theory for weak Hopf algebras, and recover analogs of classical
results for Hopf algebras. Our methods are based on the recently introduced Galois theory …

Using the theory of corings, we generalize and unify Morita contexts introduced by Chase
and Sweedler [Hopf Algebras and Galois Theory, in: Lecture Notes in Math., vol. 97 …

El Kaoutit and Gómez-Torrecillas introduced comatrix corings, generalizing Sweedler's
canonical coring, and proved a new version of the Faithfully Flat Descent Theorem. They …

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 …

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 …

Galois comodules of a coring are studied. The conditions for a simple comodule to be a
Galois comodule are found. A special class of Galois comodules termed principal …

Weak coalgebra-Galois extensions are studied. A notion of an invertible weak entwining
structure is introduced. It is proven that, within an invertible weak entwining structure, the …