A new way to iterate Brzezi\'nski crossed products

TL;DR

This paper introduces a novel method for constructing Brzeziński crossed products by combining two such products with a linear map, generalizing the iterated twisted tensor product of algebras.

Contribution

It presents a new approach to iterate Brzeziński crossed products using a linear map, expanding the framework for algebraic constructions.

Findings

Constructs a new Brzeziński crossed product from two existing ones.

Generalizes the iterated twisted tensor product of algebras.

Provides conditions under which the new product is well-defined.

Abstract

If $A\otimes _{R, \sigma }V$ and $A\otimes _{P, \nu }W$ are two Brzezi\'nski crossed products and $Q:W\otimes V\rightarrow V\otimes W$ is a linear map satisfying certain properties, we construct a Brzezi\'{n}ski crossed product $A\otimes _{S, \theta }(V\otimes W)$. This construction contains as a particular case the iterated twisted tensor product of algebras.