Hi!

Let R,S be rings and f:R-->S be a ring homomorphism. If R,S are base
rings of, e.g., matrix rings or polynomial rings, shouldn't it be
possible to construct the homomorphism of the "bigger" rings induced
by f? But how?

For example,
 sage: R.<x> = QQ[]
 sage: MS = MatrixSpace(R,2,2)
 sage: P.<y> = R[]
 sage: f = R.hom([2*x],R)
How does one create the endomorphisms of MS and P induced by f?

On a related note, how does one create a homomorphism of a Laurent
polynomial ring? I tried this:
 sage: R.<x> = LaurentPolynomialRing(ZZ)
 sage: f = R.hom([x],R)
 ERROR: An unexpected error occurred while tokenizing input
 The following traceback may be corrupted or invalid
 The error message is: ('EOF in multi-line statement', (4, 0))
 ...
 TypeError: images do not define a valid homomorphism

So, can one even not create the identity morphism?

Best regards,
Simon

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