Abstract
We consider two new algebras from an H-biquasimodule algebra A and a Hopf quasigroup H: twisted smash product A â H and L-R smash product AâH, and find necessary and sufficient conditions for making them Hopf quasigroups. We generalize the main results in BrzeziĆski and Jiao [5] and Klim and Majid [9]. Moreover, if H is a cocommutative Hopf quasigroup, we prove that A â H is isomorphic to AâH as Hopf quasigroups.
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