UC modules with respect to a torsion theory

In this paper, we give some characterizations of modules M over a ring R such that every submodule has a unique closure relative to a hereditary torsion theory on Mod-R by using the concept of tau-closed submodule which was studied in [2]. We compare UC and tau-UC modules and examine the relationships between them. We also give some examples of tau-UC and UC modules and submodules which have a unique tau-closure and unique closure.