Several Kinds Of Menon Identities On Rings Of Rational Integers

This thesis mainly focuses on some generalizations of Menon identity in the ring of integers.In Chapter 1,we give main research findings and introduction about their back-ground.In Chapter 2,we provide a list of basic definitions and significant theorems,which pave the way for the following discuss.In Chapter 3,In 1965,Menon verifies Menon identity.In 1978,there is a conclu-sion called Arai-Carlitz identity,which is a special case of V.S.Ramaiah results.In 2005,P.Haukkanen gained the Menon identity with respect to a generalized divisibity relation.In 2009,B.Sury extended the Menon identity to multiple vari-ables by using the Burnside lemma.In 2017,Zhao-Cao proved the Menon-type identities with Dirichlet characters.In 2018,Li-Kim promoted the Menon-type identities with additive characters.Inspired by these theorems,we consider four Menon-type identities in the ring of integers on the basis of Arai-Carlitz identity.