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Self-dual abelian Higgs system, involving both the Maxwell and Chern-Simonsterms are obtained from Carroll-Field-Jackiw theory by dimensional reduction.Bogomol'nyi-type equations are studied from theoretical and numerical point ofview. In particular we show that the solutions of these equations areNielsen-Olesen vortices with electric charge.

Self-dual Maxwell-Chern-Simons solitons from a Lorentz-violating model