On Weak Maps of Ternary Matroids

LetMandNbe ternary matroids having the same rank and the same ground set, and assume that every independent set inNis also independent inM. The main result of this paper proves that ifMis3-connected andNis connected and non-binary, thenM = N. A related result characterizes precisely when a matroid that is obtained by relaxing a circuit-hyperplane of a ternary matroid is also ternary.