In this paper, we present results concerning orthogonality in Hilbert C∗-modules. Moreover, for a C∗-algebra A, prove theorems the multi-A-linearity and its preservation byA-linear operators. New version of solution equation on C∗-modules mappings preserving are also investigated.

It is shown that the metric on union of sets X and Y defines a Hilbert $C^*$ -module over uniform Roe algebra space with fixed dX. A number examples such -modules are described.