Transference and preservation of uniqueness

Motivated by the notion of a set of uniqueness in a locally compact group $G$, we introduce and study ideals of uniqueness in the Fourier algebra $A(G)$ of $G$, and their accompanying operator version, masa-bimodules of uniqueness. We establish a transference between the two notions, and use this result to show that the property of being an ideal of uniqueness is preserved under natural operations.