Sanhedrin 57: Can a Non-Jew Be Subject to Jewish Law?

More on the Noahide Laws - and the puzzling nature of law for people who are not necessarily paying any attention to Torah's requirements for them. Plus, some contrasts between the Noahide law an ramifications as compared to the Jewish legal system, for example. Also, the academy of the Bnei Menashe, who have a different list. Plus, are women part of the Noahide judicial system? Also, the biblical textual support that includes a non-Jew in the Jewish legal system -- for example, if a non-Jew violated an prohibited illicit sexual relationship with a Jewish woman, who is then tried in the Jewish system.