On a class of hereditary crossed-product orders

TL;DR

This paper provides simple criteria based on two-cocycles to determine when hereditary crossed-product orders over discrete valuation rings are maximal, refining understanding of their structural properties.

Contribution

It introduces straightforward, cocycle-based criteria for identifying hereditary and maximal crossed-product orders, simplifying previous complex methods.

Findings

Criteria involve only the two-cocycle associated with the order.

Conditions effectively distinguish hereditary from maximal orders.

Simplifies analysis of crossed-product orders over valuation rings.

Abstract

In this brief note, we revisit a class of crossed-product orders over discrete valuation rings introduced by D. E. Haile. We give simple but useful criteria, which involve only the two-cocycle associated with a given crossed-product order, for determining whether such an order is a hereditary order or a maximal order.