A characterization of one-to-one modular mappings

We deal with modular mappings as introduced by H.J. Lee and J.A.B. Fortes (1994) and we build upon their results. Our main contribution is a characterization of one to one modular mappings that is valid even when the source domain and the target domain of the transformation have the same size but not the same shape. This characterization is constructive, and a procedure to test the injectivity of a given transformation is presented.