  In a previous paper, we developed a table of components of algebraic
solutions of a system of equations generated by an inhomogeneous proper-value
equation involving K\"ahler's total angular momentum. This table looks as if it
were a representation of real life quarks. We did not consider all options for
solutions of the system of equations that gave rise to it. We shall not,
therefore, claim that the present distribution of those components as a well
ordered table has strict physical relevance. It, however, is of great interest
for the purpose of developing methodology, which may then be used for other
solutions. We insert into our present table concepts that parallel those of the
phenomenology of HEP: generations, color, flavor, isospin, etc. Breaking then
loose from that distribution, we consider simpler alternatives for algebraic
"quarks" of primary color (The mathematics speaks of each generation having its
own primary color). We use them to show how stoichiometric argument allows one
to reach what appear to be esthetically appealing idempotent representation of
particles for other than electrons and positrons (K\"ahler already provided
these half a century ago with idempotents similar to our hypothetical quarks).
We then use neutron decay to obtain formulas for also hypothetical algebraic
neutrinos and the $Z_{0}$, and use pair annihilation to obtain formulas for
gamma particles. We go back to the system of equations and develop an
alternative option. We solve the system but stop short of studying it along the
present line. This will thus be an easy entry point to this theory by HEP
physicists, who will be able to go aster and further.
