Rational Modules for Corings

TL;DR

This paper develops the theory of rational modules for corings over arbitrary rings, extending coalgebra results and applying to categories like Doi-Koppinen modules, broadening their algebraic framework.

Contribution

It generalizes the concept of rational modules from coalgebras to corings over arbitrary rings and applies these results to various categories of entwined modules.

Findings

Extended rational module theory to corings over arbitrary rings

Generalized results for Doi-Koppinen and related modules

Provided a unified framework for entwined module categories

Abstract

In this paper we lay the basis of the theory of rational modules of corings extending results on rational modules for coalgebras to the case of arbitrary ground rings. We apply these results mainly to categories of entwined modules (e.g. Doi-Koppinen modules, alternative Doi-Koppinen modules) generalizing results of Y. Doi, M. Koppinen and C. Menini et al. on the categries of Doi-Hopf moduels and categories of relative Hopf modules.