A remark on the Galois-type correspondence between ideal coideals and comodule subrings of a Hopf algebroid

TL;DR

This paper establishes a bijective correspondence between ideal coideals and coideal subrings in Hopf algebroids, extending known results and providing a deeper understanding of their algebraic structure.

Contribution

It improves and generalizes a recent result by establishing a bijective correspondence in the setting of Hopf algebroids and Hopf algebras.

Findings

A bijective correspondence between certain ideal coideals and coideal subrings.

Extension of known cases in Hopf algebra theory.

Enhanced understanding of the algebraic structure of Hopf algebroids.

Abstract

We exhibit a bijective correspondence between certain left ideal coideals in a Hopf algebroid for which the resulting quotient is a coequalizer and certain right coideal subrings which are themselves an equalizer, remarkably improving a recent result of the author obtained in collaboration with L. El Kaoutit, A. Ghobadi and J. Vercruysse. Interpreting this result in the Hopf algebra setting provides a bijective correspondence which extends the previously known cases.