Crossed Products by Twisted Partial Actions: Separability, Semisimplicity, and Frobenius Properties

Abstract

In this article, we are concerned with the crossed product S = R☆_α G by a twisted partial action α of a group G on a ring R. We give necessary and sufficient (resp., sufficient) conditions for S to be a separable (resp., Frobenius, semisimple) extension of R.

Key Words:

• Crossed product
• Frobenius extension
• Semisimple extension
• Separable extension
• Twisted partial action

2000 Mathematics Subject Classification:

• 16H05
• 16S35
• 16W22

ACKNOWLEDGMENT

This article was partially supported by CAPES (Brazil).

Notes

Communicated by I. Shestakov.