The consecrated [offerings] of non-Jews — one is not liable for them for piggul, nossar, or tamei; and one who slaughters them outside [the Temple] is not liable; [these are] the words of R’ Meir. R’ Yose declares him liable. Things for which one is not liable for piggul, one is [still] liable for them for nossar, [and] for tamei; except for the blood. R’ Shimon says: For things which are usually eaten; but [for] the likes of wood, frankincense, and incense, one is not liable for them for tumah.

A sacrifice is slaughtered for the sake of six things: for the designation of the sacrifice, for the name of [the] offerer, for the Name of Hashem, for the sake of the fires, for the sake of aroma, for the sake of pleasing; and the chatas- and asham-offerings for the purpose of [the] sin. Said R’ Yose: Even if one did not have any of these [purposes] in mind it is valid, for it is an enactment of the Court, because the intent is determined solely by the one who performs the service.