Demai, Chapter One, Mishnah Three
This mishnah teaches that the rules of demai apply only to cases where a person bought produce from an am haaretz in order to use it for food. If he bought the produce for another purpose, such as to feed his animals, then he need not separate out tithes.
1) If a man bought [grain from an am haaretz] to be used for seed or for animal [feed], flour for hides, oil for a lamp, or oil for greasing utensils, it is exempt from [the rules of] demai.
2) [Produce grown] beyond Cheziv and north is exempt from [the rules of] demai.
3) The hallah of an am haaretz, produce mixed with terumah, produce bought with second tithe money, and the leftovers of minhah offerings are exempt from [the rules of] demai.
4) Oil spiced [with spices from an am haaretz]:
a) Bet Shammai makes it liable [to the rules of demai].
b) But Bet Hillel exempts it.
Section one: In these scenarios a person buys produce from an am haaretz but does not intend to use it as food. The mishnah rules that he need not separate tithes because even in cases of produce that has definitely not been tithed but is to be used for non-food, there is only a rabbinic law mandating that tithes be separated. From the Torah, such produce is exempt from tithes.
Section two: Cheziv, or Achziv (Joshua 19:29), is in the northern part of Israel and is not considered to be part of the land of Israel. Produce from Cheziv and north is exempt from tithes, and certainly the laws of demai do not apply.
Section three: There are four things listed in this section each of which is exempt from the rules of demai.
1. Hallah is a part of the dough separated and given to the priest (we shall have an entire tractate on this subject). The mishnah refers to the hallah of an am haaretz that he separated and gave to a priest.
2. Produce mixed with terumah refers to non-sanctified produce of an am haaretz that becomes mixed up with terumah. This mixture can only be eaten by priests.
3. Produce bought from an am haaretz with second tithe money.
4. The left-over minhah offerings of an am haaretz.
In the Talmud Yerushalmi there is a debate over why these things are exempt from demai. According to one opinion, when the rabbis decreed that one must separate tithes from produce bought from an am haaretz, they did not include these things in the decree. The other opinion is that because these things have some extra holiness, we can assume that the am haaretz would have tithed them.
Section four: According to Bet Shammai, although spiced oil is meant for anointing and not for food, it is still subject to the laws of demai. According to Bet Hillel, it is exempt.