LAUSR

This paper introduces and investigates Ore extensions in the context of multiplier Hopf coquasigroups, a structure that generalizes both multiplier Hopf algebras and Hopf coquasigroups. We establish necessary and sufficient conditions under which an Ore extension of a regular multiplier Hopf coquasigroup itself forms a regular multiplier Hopf coquasigroup. Furthermore, we explore the isomorphism problem for such Ore extensions, providing criteria for the equivalence of two extensions. The case of multiplier Hopf coquasigroups is also analyzed, with conditions derived for the Ore extension to inherit the structure. Our results unify and extend prior work on Ore extensions in the settings of Hopf algebras, multiplier Hopf algebras, and Hopf coquasigroups.