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Let $R$ be a commutative ring with the identity.  A ring $R$ is clean if any element of $R$ can be expressed as a sum of idempotent and unit element \cite{nicholson1,anderson1}. Any $R$ is a module over itself \cite{kasch, adkins} and the endomorphism ring of $R$-module $R$ ($End_{R}(R)$) is isomorphic to $R$ \cite{wisbauer1,anderson2,lam}.  By using cleanness concept on rings, any $R$-module $M$ is said to be clean if the endomorphism ring $End_{R}(M)$ is a clean ring \cite{nicholson2,nicholson3,camillo}.\\The cleanness of coalgebras and comodules is defined in \cite{puspita1,puspita2}. A right $C$-comodule $M$ is clean if the endomorphism ring of $C$-comodule $M$ ($End^{C}(M)$) is clean. The clean coalgebras  define as a special condition of clean comodules when $M=C$. Here,  $R$ is a clean ring if and only if $R$ is a clean trivial $R$-coalgebra and $M$ is a clean $R$-module if and only if $M$ is a clean trivial comodule over $R$. In general, a clean ring is not automatically become a clean coalgebra. We define clean Hopf modules and clean bialgebras. Based on the cleanness properties of the trivial comodules, we have cleanness relations on the category of rings, modules, comodules, and Hopf modules. We proved that the ring $R$ is clean if and only $R$ is a bialgebra over itself, and $M$ is a clean module if and only if $M$ is a trivial Hopf module over bialgebra $R$.\\