Many observations about coalgebras were inspired by comparable situations for algebras.
Despite the prominent role of prime algebras, the theory of a corresponding notion for …

The theory of general Galois-type extensions is presented, including the interrelations
between coalgebra extensions and algebra (co) extensions, properties of corresponding …

We introduce the notion of a partial corepresentation of a given Hopf algebra H over a
coalgebra C and the closely related concept of a partial H-comodule. We prove that there …

We unify and generalize different notions of local units and local projectivity. We investigate
the connection between these properties by constructing elementary algebras from locally …

The main aim of this paper is to give a Hopf algebroid approach to the Picard-Vessiot theory
of linear differential matrix equations with coefficients in the polynomial complex algebra. To …

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 …

This paper contributes to the characterization of a certain class of commutative Hopf
algebroids. It is shown that a commutative flat Hopf algebroid with a non zero base ring and …

We construct comatrix corings on bimodules without finiteness conditions by using firm rings.
This leads to the formulion of a notion of Galois coring which plays a key role in the …

We show the close connection between apparently different Galois theories for comodules
introduced recently in [J. Gómez-Torrecillas and J. Vercruysse, Comatrix corings and Galois …

We propose a class of infinite comatrix corings, and describe them as colimits of systems of
usual comatrix corings. The infinite comatrix corings of El Kaoutit and Gómez Torrecillas are …