This text is the third volume in the series "Loop Transformations for Restructuring Compilers". This series has been designed to provide a complete mathematical theory of transformations that can be used to automatically change a sequential program containing FORTRAN-like do loops into an equivalent parallel form. In this text the author extends the model to a program consisting of do loops and assignment statements, where the loops need not be sequentially nested and are allowed to have arbitrary strides. In the context of such a program, the author studies, in detail, dependence between statements of the program caused by program variables that are elements of arrays.