I have to study systems of equations in a Boolean algebra, the matrix is $m\times n$ with $m\neq n$. The Boolean algebra is actually the simplest one, it contains only $0$ and $1$, let us denote it by $\mathbb{B}$. What I need to know is a necessary and sufficient condition for an application from $\mathbb{B}^m$ to $\mathbb{B}^n$ to be one-to-one. I read in the paper "Linear Boolean Equations and Generalized Minterms" by S. Rudeanu (Discrete Math 43 (1983) 241-248) that Löwenheim proved some theorems in the case $m=n$ in a paper written in 1919. Hence my question :

Is there any more recent reference about this subject (systems of equations in Boolean algebra) and also in the case $m \neq n$ ? And where can I find a proof of Löwenheim's theorem (that could help to understand) ?

All references I can found in some papers I can find (with difficulty) on the Web are unavailable online, and unavailable in my library.