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The so-called “invariance under twisting” for twisted tensor products of algebras is a result stating that, if we start with a twisted tensor product, under certain circumstances we can “deform” the twisting map and we obtain a new twisted tensor product, isomorphic to the given one. It was proved before that a number of independent and previously unrelated results from Hopf algebra theory are particular cases of this theorem. In this article we show that some more results from literature are particular...

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