The meaning of their (B’Nai Noach) obligation of dinim is that they are required to established laws of honesty and right behavior; they are not bound by the laws of the Bible except those that were commanded explicitly (e.g. prohibition of murder, etc.). That which Israel was commanded, to judge between one man and another, was not addressed to the descendants of Noah. (Hazon Ish, Baba Kama 10:3)

And it is clear that their (B’nai Noach) dinim are not meant to be the laws of the Torah, but rather convention. And although there are those who have investigated this extensively, the truth is as I have written, and there is no need to go any further length on this matter.” ( R. Yehi’el Mikhel Epstein, Arukh haShulhan he’Atid, Hilkhot Melakhim 79:15. )

This seems to support those authorities who have argued against Rema’s holding that, in practice, we rule according to R. Yitzhak who infers dinim from Elohim, and that consequently descendants of Noah must judge according to the laws of the Torah…On the contrary, it is accepted that according to all opinions in the Talmud, descendants of Noah need give judgment in accordance with convention only, not biblical law.
(R. Meir Dan Plotzki, Hemdat Yisrael, Kuntres Ner Mitzvah, p. 99b.)

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Perhaps dinim is different, for there is a great difference between their laws, which are based upon human understanding, and the laws of Israel, which were given by God at Sinai. Thus it is proper to declare in the benediction, “Who commanded us,” since He has not dealt so with any other nation; and as for His ordinances, they have not known them. (R. Tzvi Pesah Frank, Har Tzvi, Orah Hayyim II, Kuntres Mili de Berakhot, he’arah to 2:1. )

And even as regards the commandments they did receive, I have already written that the details of these commandments were not communicated to them. And this is certainly the case with regard to the commandment of dinim in which they were commanded simply to establish courts as in Sanhedrin 56b, and as explained by Maimonides Hilkhot Melakhim 9:14). And although Nahmanides differed with Maimonides, holding that with regard to the specifics of their laws they are bound to judge after the fashion of the laws of Israel, it seems clear that his intention is to say that just as in the case of Israel, for whom the basis of the commandment of dinim is the obligation of every individual to obey the laws, so also for descendants of Noah, the obligation is for each individual to act in accordance with the law. For Maimonides, on the other hand, the commandment of dinim is only that of establishing courts. Thus, a Noahide may not be executed for failing to obey the law, since it is not one of the seven commandments. Hence, even according to Nahmanides, the particulars of Noahide law may certainly differ from those of Jewish law. The operative principle of Jewish law is the holiness of the Torah, while Noahide law is based up the dictates of basic human honesty. (R. Avraham Kook, Etz Hadar, chap. 40, text to n.11.)

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