Some tools for my personal research of a particular near-ring over free groups generated by a numbers of symbols. Each symbol is associated with a certain number, like in some classical numerical systems (Greek, Hebrew, Syriac, Arabic Abjad numerals).
Since concatenation (which serves as the addition in free groups) is non-commutative, the multiplication is only distributive on the right, hence it's a near-ring, although it does contain an infinite number of isomorphisms of the integer ring as subrings.
For simplicity of coding, the generator set of symbols is for the time being represented as numbers.