Gemara

53b (Rav Yehudah): If a Yisrael erected a brick and never bowed to it, but a Nochri bowed to it, it is forbidden.

(R. Elazar): We learn from the conquest of Eretz Yisrael. The Torah commanded "va'Ashereihem Tisrefun ba'Esh";

Question: Why were the Asheiros forbidden? Bitul helps for Asheiros from before the Avos. The Torah would not command to burn them! After the Avos, Eretz Yisrael belonged to Yisrael. One (a Nochri) cannot forbid what he does not own!

Answer: When Yisrael served the Egel, they showed approval of idolatry, and consented to worship of Asheiros in Eretz Yisrael.

54a (Beraisa): If one worshipped his own animal, it is forbidden. If he worshipped another's animal, it is permitted.

Contradiction (Beraisa): Whether an animal was Ne'evad b'Mezid or b'Shogeg, willingly or b'Ones (under compulsion), it is forbidden.

Suggestion: Ones is when Levi stole Reuven's animal and worshipped it.

Answer #1 (Rav Ada bar Ahavah): The case is, Levi poured wine between the horns of Reuven's animal to serve it. Since he did an action to it, he forbids it;

(Ula citing R. Yochanan): Even though one who bows to another's animal does not forbid it, if he did an action to it, he forbids it.

(Rav Nachman citing Rav Huna): R. Yochanan discusses when the animal was lying in front of idolatry, and Levi slaughtered one Siman (the windpipe or foodpipe). It is forbidden.

54b: We learn from Kelim that Achaz used for idolatry.

"Ha'Kelim Asher Hizni'ach Melech Achaz... Hechanu (we buried them) v'Hikdashnu." Even though Achaz did not own them (they were Hekdesh), because he did an action to them, he forbade them. Likewise, one who does an action to another's animal forbids it.

(Rav Dimi citing R. Yochanan): One who bows to land (untouched by man) does not forbid it, but if he digs pits in it for the sake of idolatry, he forbids it.

Chulin 40b (Rav Nachman, Rav Amram, R. Yitzchak): One cannot forbid another's property.

Question (Mishnah): If two slaughtered together, and one intended for idolatry, and the other intended for proper Shechitah, the Shechitah is invalid.

Answer: No. The case is, they are partners in the animal.

Suggestion: Rav Huna and Rav Nachman argue like the following Tana'im argue.

(Beraisa): If a Nochri was Menasech a Yisrael's wine not in front of an idol, the wine is forbidden;

R. Yehudah ben Beseira and R. Yehudah ben Bava permit, for Nisuch is only in front of an idol, and one cannot forbid what is not his.

Rejection: Rav Nachman can hold like the first Tana. Only a Nochri forbids someone else's property. If a Yisrael was Menasech, we assume that he did not really intend for idolatry, rather to vex the owner of the wine.

Question (Mishnah): If two slaughtered together, and one intended for idolatry, and the other intended for proper Shechitah, the Shechitah is invalid.

Answer: The case is, the one with forbidden intent is a Mumar.

Question (Rav Acha brei d'Rava): If Levi was warned just before he was Menasech Shimon's wine, and he replied 'I do so, accepting that I will be executed for this', what is the law?

Answer (Rav Ashi): The wine is forbidden. This is the ultimate case of a Mumar!

Rishonim

Rosh (Chulin 2:14): Even though one who bows to another's animal does not forbid it, if he did an action to it (for idolatry), he forbids it. Rav Nachman, Rav Amram, and R. Yitzchak say that one cannot forbid another's property. Rashi explains that this is even through a major action, for we challenge this from Metamei, Medame'a and Menasech. R. Chananel says that they permit only if a small action was done. They argue about a major action. With difficulty, we can say that (Metamei, Medame'a or) Menasech is not considered a major action, because the damage is not visible. Presumably, Rashi is correct. Even though one need not pay for unnoticeable damage, regarding Isur he did a great action. The Gemara concludes that Rav Yehudah (Ma'adanei Yom Tov - this should be 'Rav Huna) and Ula hold like the first Tana, unlike R. Yehudah ben Beseira and R. Yehudah ben Bava, but the law of Rav Nachman, Rav Amram, and R. Yitzchak is even like the first Tana. Only a Nochri forbids another's property. A Yisrael does not, even if he is a partner, for he merely intends to pain the owner. The Halachah follows them, for we establish their law like everyone. A Mumar, or one who was warned and accepted the warning, forbids another's property.

Beis Yosef (YD 145 DH u'Mah): Also the Ran and Tur rule like Rashi, unlike R. Chananel.

Rambam (Hilchos Avodah Zarah 8:1): If one slaughtered another's animal to idolatry, or exchanged it (for idolatry), he did not forbid it, for one cannot forbid another's property.

Rebuttal (Ra'avad): One can forbid another's property through an action, like Rav Huna taught. We hold like him; the Halachah follows the Sugya in Avodah Zarah. This refers to a Nochri or a Yisrael Mumar. A regular Yisrael merely intends to pain the owner.

Kesef Mishneh: The Rambam rules like Rav Nachman, Rav Amram, and R. Yitzchak. However, why didn't he distinguish between a regular Yisrael and a Nochri or Mumar, and whether he is a partner? It seems that he relied on what he wrote in Hilchos Shechitah (2:21).

Ran (8b DH Garsinan): If one slaughters another's animal to idolatry, one may benefit from it. However, some forbid eating it. Regarding eating, we do not say that one cannot forbid another's property. He does not forbid it; rather, he does not permit it. It is as if it died without slaughter.

Ramban (Avodah Zarah 53b DH v'Iy): Why does Bitul help for Asheiros from before the Avos? Perhaps they were served through an action! Rav Yehudah must hold that no action can forbid another's property. I say that Bitul helps even for Asheiros after the Avos. Even though Eretz Yisrael belonged to Yisrael, since the Nochrim served them Bal Korcho (against the will) of the owners, it is as if they were of the Nochrim. Even though Bitul does not help for a Nochri's idolatry that a Yisrael acquired, here it helps, for it was served Bal Korcho of the owner through theft, regarding Isur it is like the Nochri's. Bitul permits it before the Yisrael acquires it (back). Alternatively, mid'Oraisa Bitul helps for a Nochri's idolatry that a Yisrael acquired. It is only mid'Rabanan that it does not help.

Rebuttal (Ran 24b DH v'Garsinan (1)): Indeed, Rav Yehudah holds that even an action cannot forbid another's property. We learn from Achaz's Kelim that Bitul never helps. This is why they buried them, and the stones of the Mizbe'ach that the Nochrim defiled. We retract form what we said above that (Bitul would permit to people, but) it was improper for a commoner to use them. If we did not retract, there is no proof from Achaz' Kelim!

Poskim

Shulchan Aruch (YD 145:8): If one slaughtered one Siman of an animal to idolatry, he forbade it, even if it is not his. Only a Nochri forbids another's property. A Yisrael does not; he merely intends to pain the owner. Some say that this is even if the Yisrael is a partner. If the Yisrael is a Mumar, or he was warned and accepted the warning, he forbids.

Shach (21): Even part of one Siman forbids.

Beis Yosef (DH u'Mah): After we answered that a Yisrael does not intend for idolatry, rather, to vex the owner, we asked from the Mishnah about two who slaughtered together, and answered that the one with forbidden intent was a Mumar. Rashi (41a DH b'Yisrael) says that we could have answered that he was a partner, like we answered above. Tosfos (DH b'Yisrael) disagrees. Why would we ask a question that was already answered?! Rather, even if he is a partner, we can say that he intended only to pain him. Also the Rosh and Tur rule like this.