Ring Theoretic Properties of Partial Crossed products and related themes

TL;DR

This paper explores various ring-theoretic properties of partial crossed products arising from unital twisted partial actions, including conditions for artinianity, noetherianity, and Frobenius properties, along with their structural implications.

Contribution

It provides a comprehensive analysis of ring properties of partial crossed products under unital twisted partial actions, extending existing theory to new classes of algebras.

Findings

Characterization of artinian and noetherian partial crossed products

Conditions for partial crossed products to be Frobenius or symmetric

Analysis of Krull dimension and homological dimensions in these algebras

Abstract

In this paper we work with unital twisted partial actions. We investigate ring theoretic properties of partial crossed products as artinianity, noetherianity, perfect property, semilocalproperty, semiprimary property and we also study the Krull dimension. Moreover, we consider triangular matrix representation of partial skew group rings, weak and global dimensions of partial crossed products Also we study when the partial crossed products are Frobenius and symmetric algebras.