possible bug: kernel of ring homomorphism

asked 2021-02-07 17:41:51 +0100

makos gravatar image

The kernel of a ring homomorphism to a quotient ring gives unexpected results:

A.<t> = QQ[]
B.<x,y> = QQ[]
H = B.quotient(B.ideal([B.1]))
f = A.hom([H.0], H)
f
f.kernel()

outputs:

Ring morphism:
  From: Univariate Polynomial Ring in t over Rational Field
  To:   Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (y)
  Defn: t |--> xbar
Principal ideal (t) of Univariate Polynomial Ring in t over Rational Field

whereas the kernel of f:A[t]->B[x,y]->B[x,y]/(y), for f(t)=x should be (0).

Why?

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Comments

slelievre gravatar imageslelievre ( 2021-02-09 03:55:39 +0100 )edit
rburing gravatar imagerburing ( 2021-02-09 15:28:59 +0100 )edit