A ring map $f \colon A \to B$ makes $B$ into a module over $A$. This method returns true if and only if this module is a finitely generated $A$-module.
i1 : kk = QQ; |
i2 : A = kk[t]; |
i3 : C = kk[x,y]; |
i4 : B = C/(y^2-x^3); |
i5 : f = map(A, B, {t^2, t^3})
2 3
o5 = map (A, B, {t , t })
o5 : RingMap A <--- B
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i6 : isWellDefined f o6 = true |
i7 : isModuleFinite f o7 = true |
i8 : f = map(kk[x,y], A, {x+y})
o8 = map (QQ[x..y], A, {x + y})
o8 : RingMap QQ[x..y] <--- A
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i9 : assert not isModuleFinite f |
If a ring $R$ is given, this method returns true if and only if $R$ is a finitely generated module over its coefficient ring.
i10 : A = kk[x] o10 = A o10 : PolynomialRing |
i11 : B = A[y]/(y^3+x*y+3) o11 = B o11 : QuotientRing |
i12 : isModuleFinite B o12 = true |