# A note on the bijectivity of antipode of a Hopf algebra and its applications

## TL;DR

This paper explores conditions under which a Hopf algebra's antipode is bijective, providing insights into the homological properties of noetherian Hopf algebras and their applications.

## Contribution

It introduces new homological and ring-theoretical criteria ensuring the bijectivity of the antipode in Hopf algebras, with applications to noetherian cases.

## Key findings

- Identifies sufficient conditions for antipode bijectivity
- Links antipode bijectivity to homological properties of Hopf algebras
- Provides applications to the study of noetherian Hopf algebras

## Abstract

Certain sufficient homological and ring-theoretical conditions are given for a Hopf algebra to have bijective antipode with applications to noetherian Hopf algebras regarding their homological behaviors.