The following is the codification of the Sanhedrin's clarification of this matter as put forth by RAMBAM in the Mishneh Torah, Hilkhoth Melakhim u'Milhamotheihem :

 

From what point in time is a Bahth Noah [a non-Jewish woman] considered divorced?  She is considered divorced from the time that she is removed from his [her husband's] home and is sent on her own, or, when she chooses to leave his domain and goes to be on her own. Their divorce is not made in writing.  This matter does not depend on the man's choice alone.  At whatever point in time that either he or she decide to separate and go their own individual ways, they are divorced.

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**Personal comments:  Although the above constitutes the authoritative definition of divorce according to the 7 Laws of Noah, there is certainly no problem in having the divorce officiallized in writing with the government.  It may even be praiseworthy.  Keep in mind, however, that such a divorce is not a real divorce simply because it is official according to the secular law and in writing.  It is possible for a couple to be divorced according to the secular law and yet still married according to the 7 Laws of Noah.  It is also possible to be married according to the 7 Laws of Noah and still unmarried according to the secular law.  Therefore, it is possible for one to commit adultery according to the 7 Laws of Noah with a woman who is 'unmarried' according to secular law, but married to another man according to the 7 Laws of Noah.  Many boyfriend/girlfriend couples are married according to the 7 Laws of Noah without realizing it.  If the girlfriend 'cheats' on her boyfriend and has relations with another guy, it is not merely cheating.  This would be actual adultery.

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It is often known among those with a Christian background that the N.T. records some comments of Jes*us on the issue of divorce and adultery.  He makes his statements based upon his understanding of Deuteronomy 24:1-5.  His statements are recorded in Matthew 5:31-32; Matthew 19:7-12; and Mark 10:4-12.  A few things should be kept in mind with regard to these statements, for one who still believes in Jes*us:

 

1)  Deuteronomy 24:1-5 is a command given to the people of Israel.  Therefore, with the context of Deuteronomy in mind, and the context of the conversation in which Jes*us makes his statements on divorce, one should understand that his statements were NOT directed to the nations of the world.  Jes*us was directing them toward the people of Israel.

 

2)  In all 3 of the places where his statements are recorded, Jes*us states that

one who divorces his wife causes adultery.  In Matthew 19:9 it seems to state that this would only be adultery if he married another woman after having divorced the previous wife without a valid reason.  Matthew 5:32 states that he makes his invalidly divorced wife commit adultery.  Then the two places in Matthew each give a different valid reason for divorce.  In Mark 10:11 it does not give a condition upon which divorce would be valid.  Mark 10:11 states that "whoever divorces his wife and marries another woman commits adultery against her;"

 

Matthew 19:9 states:

"whoever divorces his wife, except for immorality, and marries another woman commits adultery."

 

Matthew 5:32 states:

"everyone who divorces his wife, except for the reason of unchastity, makes her commit adultery;"

 

Besides the impossible question on Mark 10:11, since in Mark Jes*us states that all divorce causes adultery and that there is no valid reason for divorce, all three of the places in the N.T. have other problems.

 

Even IF a man would be forbidden to divorce his wife for any reason at all, or would only be permitted to divorce her for her having been unchaste or immoral, there is no way in Torah law by which a man divorcing his wife for an invalid reason would cause him to be committing adultery by marrying another woman, even if his divorce from the first wife is invalid.  While he may technically still be married to the first woman, this does not make it forbidden to him to marry another woman, so long as this second woman is not married.  Whether or not having multiple wives is preferable, it is certainly not prohibited.  In certain cases it is even commanded.  This leads me to think that either some later individual(s) edited the texts of the N.T. or that the N.T. writers wrote Jes*us statements based on corrupted traditions, or... that Jes*us was either horribly ignorant of Torah law or that he was not ignorant but was simply flat out rebelling against it.  The only other option is that he was simply insane.  From the inconsistencies in the texts concerning his statements on this issue, it seems obvious that his statements have been distorted, whatever his original statement was.

 

The only valid worry, IF Jes*us understanding of Deuteronomy 24:1-5 were accepted as real Jewish law, is his statement that the husband causes his divorced wife to commit adultery.  This would only be adultery if the ''divorced'' wife 'married' another man, assuming that her ''divorce'' from her first husband was invalid.  There is no adultery in Torah law between a Jewish man and an unmarried woman, whether the man is married or unmarried.  In such a case there may be other prohibitions, but they do not concern adultery.  Adultery in Jewish law is only between a man and a MARRIED WOMAN.  The same in this regard is true for b'nay Noah [sons of Noah/non-Jews] as well.