# Globalization of partial cohomology of groups

## TL;DR

This paper investigates the connection between partial and global group cohomology, demonstrating that under certain conditions, partial cocycles can be extended to global cocycles, thus linking local and global algebraic structures.

## Contribution

It proves that partial cocycles are globalizable when the algebra is a product of indecomposable rings under a unital partial group action.

## Key findings

- Partial cocycles are globalizable in the specified setting.
- The result applies to group actions on direct products of indecomposable rings.
- Bridges the gap between partial and global cohomology theories.

## Abstract

We study the relations between partial and global group cohomology with values in a commutative unital ring $\mathcal{A}$. In particular, for a unital partial action of a group $G$ on $\mathcal{A}$, such that $\mathcal{A}$ is a direct product of commutative indecomposable rings, we show that any partial $n$-cocycle of $G$ with values in $\mathcal{A}$ is globalizable.