My question: what if the husband before dying left semen for artificial insemination.
Would this be permitted after his death if there was a potential miyavem?
The two sides of the argument:
NOT PERMITTED
Arificial insemination would not be permitted because she is now a yivama at the time of death (having no fetus or child) so she must be taken care of (yivum or chaliza);
PERMITTED
the semen is considered as potential having a child and is included in "v'zera ein lah, ayin alav).
shlomo flam
Your question assumes that the child which results from artificial insemination is Meyuchas to the man from whom the semen was extracted. Contempory Poskim differ on this issue.
Assuming that it is, the question may be rephrased as follows: There is a less exotic possibility for a woman to become impregnated after the death of her husband, for the Gemara says that the Zera can be Niklat until three days after the Bi'ah. In such a case she would have to wait for she may end up to be an Ervah of Eishas Ach with children. If so we have a precedent for posthumous impregnation.
However, the verse "Ayin Alav" (which teaches that a pregnant woman cannot undergo Yibum) relates only to a woman who is actually pregnant (and perhaps will give birth), not to a woman who could be made to become pregnant. Therefore it is likely that the woman will be permitted to undergo Yibum.
Dov Zupnik