University of MaraghehSahand Communications in Mathematical Analysis2322-580709120180101On the cyclic Homology of multiplier Hopf algebras1131282364510.22130/scma.2018.23645ENGhorbanali HaghighatdoostDepartment of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.Hami Abbasi MakraniDepartment of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.Rasoul MahjoubiDepartment of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.Journal Article20160306In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ consisting of a regular multiplier Hopf algebra $mathcal{H}$, a left $mathcal{H}$-comodule algebra $mathcal{R}$, and a unital left $mathcal{H}$-module $mathcal{X}$ which is also a unital algebra. First, we construct a paracyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ and then prove the existence of a cyclic structure associated to this triple.http://scma.maragheh.ac.ir/article_23645_980a6fd18602b47503b690dd49acad52.pdf