Like Jews, non-Jews may not eat “eiver min hachai,” a limb torn from a live animal. This law was stated explicitly to Noah in Genesis 9:4. This mitzvah is the one that may or may not have been commanded to Adam.
In Genesis 9:3, Noah was given permission to slaughter animals for food, something that had been forbidden to previous generations. If Adam was a vegetarian, then of course eiver min hachai is a moot point. But was Adam a vegetarian? He couldn’t slaughter a lamb for food, but what if he found one that had been killed by a lion? Could he eat it? If so, then eiver min hachai would apply to a limb lost by an animal in an accident. (See Tosfos on Sanhedrin 56b.) Rashi on Genesis 37:2, that Joseph spoke badly of his brothers, explains that he accused them of eating a limb torn from a live animal, among other things. Rashi does not explain, however, how such a misunderstanding could take place. Well, it goes like this: a difference between this halacha for Jews and non-Jews involves meat taken from an animal after it is slaughtered but before it is actually dead. The halacha is that this meat is not considered eiver min hachai for Jews but non-Jews must wait until the animal is completely dead before removing any meat. (This is because shechitah, ritual slaughter, is only a mitzvah for Jews.) Joseph’s opinion was that, before the Torah was given, Jacob’s sons were halachically non-Jews and meat taken after slaughter was forbidden to them. His brothers felt that they were halachically Jews, so that meat taken after slaughter was permitted to them.
For a far more in-depth and advanced study of all the Seven Noahide Laws consider taking the Noahide Laws Yeshiva Course.