Bechorot 3: Co-Ownership of a Donkey by a Jew and Gentile - How to Manage Bechor

Massechet Bechorot is about bechor, the redemption of the firstborn.  Our first daf began with a Mishna regarding a firstborn donkey, a non-kosher animal.  If a Gentile owns an animal, it is not subject to the laws of bechor.  These include a firstborn male that must be redeemed by his father, a firstborn male animal that is sanctified from birth and thus must be sacrifice, and a firstborn male donkey that must be exchanged for a lamb for sacrifice by a kohen.

Today we learn about a circumstance where a Jew and a Gentile co-own the animal.  Rabbi Yehuda orders that the Jew is obligated to pay half of the value of the firstborn to a kohen.  The Sages argue that the animal is entirely free from the laws of bechorot.  Rav Huna says that even if the Gentile only owns the animal's ear, there is not mitzvah of bechor.

The Geara teaches about a woman who converted to Judaism whose gentile brothers gave her animals to fatten and then would divide the profits with her.  She came to Rava to confirm her obligation regarding bechorot.  Rava told her that there is no authority that pays any attention to Rabbi Yehuda's ruling that an animal co-owned by a Jew and a Gentile is subject to the laws of the bechor.

Steinsaltz adds that conversion to Judaism was infrequent in Babylonia.  The Persian government discouraged such behaviour.  Regardless, during Rava's time (the reign of Shevor Malka - Shapur) we learn about a number of conversions taking place in Rava's hometown of Mechoza.  It is suggested that this might be connected to the positive relationship between the Shevor Malka, the kind, and the Jewish community leaders in Babylonia at this time.