definitely pursue it.
i’ve had a few approaches myself.
my favorite was seeing the relationship between chinese reminder theorem and all programming structures. (because mod math is rotation, and computer programs are all rotation. in order to even compile they have to be logically sound on a “line by line” basis in structure regardless of its visual output and all computer hardware can be realized in software and all software can be realized in hardware.
so having chinese remainder theorem for the ideal ring it let me use time (which algorithms need) to ultimately fulfill the gap from 0 to 1, making an ideal ring.