# baseRing -- produce the ring from which a ring was formed

## Synopsis

• Usage:
baseRing R
• Inputs:
• Outputs:
• a ring, the ring from which
• R
• was formed

## Description

The base ring of a ring R is the ring from which R was formed. For example, if R is a quotient ring of the form S/I, or if R is a fraction ring of the form frac S, or if R is a polynomial ring over S, then the base ring is S.

 i1 : baseRing QQ o1 = ZZ o1 : Ring i2 : R = QQ[x,y] o2 = R o2 : PolynomialRing i3 : S = R / (x^2 + y^3 - 1) o3 = S o3 : QuotientRing i4 : T = frac S o4 = T o4 : FractionField i5 : baseRing T o5 = S o5 : QuotientRing i6 : baseRing S o6 = R o6 : PolynomialRing i7 : baseRing R o7 = QQ o7 : Ring

The entire chain of base rings can be obtained under the key baseRings.

 i8 : T.baseRings o8 = {ZZ, QQ, R, S} o8 : List