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InducedHom

homomorphism induced by a homomorphism

Syntax
InducedHom(RmodI: RING, phi: RINGHOM): RINGHOM

Description
InducedHom(R, phi) -- where R is a QuotientRing, gives the homomorphism R/I into S induced by phi: R into S (which must have the base ring of RmodI as its domain, and whose kernel must contain the defining ideal of RmodI) InducedHom(FrF, phi) -- may be partial where FrF is a FractionField, gives the homomorphism induced by phi (which must have the base ring of FrF as its domain). Note that the resulting homomorphism may be only partial (e.g. if ker(phi) is non-trivial, or if the codomain is not a field).

Example
/**/ Use R ::= QQ[x,y];
/**/ RmodI := NewQuotientRing(R, ideal(x^2-1));

/**/ Use S ::= QQ[a,b,c];
/**/ SmodJ := NewQuotientRing(S, ideal(a^2-1));

/**/ phi := PolyAlgebraHom(R,S,[a,b]);
/**/ Use R;
/**/ phi(x);
a
/**/ psi := InducedHom(RmodI, CanonicalHom(S,SmodJ)(phi));
/**/ Use RmodI;
/**/ psi(x);
(a)

See Also