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Ol' Don Goldberg Had a Field (1980?)

(to the tune of Old MacDonald)

Ol' Don Goldberg had a field, e+1
In that field there was a ring, e+1
With a product here, and a prime divisor there
p is prime, UFD, p divides a or b
Ol' Don Goldberg had a field, e+1

Ol' Gon Doldberg had some stamps, e+1
Their GCD was seventeen, e+1
With an Ax here and a By there
Ax, By, mail a letter anywhere
Ol' Gon Doldberg had some stamps, e+1

Ol' Gol Donberg had a group, e+1
The group had order phi of n, e+1
With a subgroup here and a generator there
Here a theorem, there a theorem, even Fermat's Little Theorem
Ol' Gol Donberg had a group, e+1

Ol' Berg Goldon had a map, e+1
And on the map there were countries, e+1
With a color here, and a color there
Takes four colors everywhere
Ol' Berg Goldon had a map, e+1

Ol' Derg BonBon had a plane, e+1
And on the plane there was a line, e+1
Off that line there was a point, e+1
Through that point a parallel, and there was but one!