We present an embedding of the three-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an N = 6, U(N) x U(N) Chern-Simons-matter theory [the Aharony-Bergman-Jafferis-Maldacena model] by consistently truncating the latter to an Abelian effective field theory encoding the collective dynamics of O(N) of the O(N-2) modes. In fact, depending on the vacuum expectation value on one of the Aharony-Bergman-Jafferis-Maldacena scalars, a mass deformation parameter mu and the Chern-Simons level number k, our Abelianization prescription allows us to interpolate between the Abelian Higgs model with its usual multivortex solutions and a phi(4) theory. We sketch a simple condensed matter model that reproduces all the salient features of the Abelianization. In this context, the Abelianization can be interpreted as giving a dimensional reduction from four dimensions.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)