If R is a polynomial ring, then the coefficient ring is the base ring from which the coefficients are drawn. If R is constructed from a polynomial ring as a quotient ring or a fraction ring or a sequence of such operatinos, then the original coefficient ring is returned.
i1 = coefficientRing(ZZ/101[a][b])
ZZ
o1 = ---[a]
101
o1 : PolynomialRing
i2 = ultimate(coefficientRing,ZZ/101[a][b])
ZZ
o2 = ---
101
o2 : QuotientRing
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