Once a divorce has been finalized, both according to the Torah, and according to State and Federal law, the offending party is free to marry again.
So, if a man commits adultery, and then gets divorced on account of the adultery, and then marries the woman with whom he has had an affair, the second marriage is sanctioned both by the Torah and State and Federal law.
As Amanah has indicated, as
Deuteronomy 24:3 shows, a divorced woman may become the wife of another man.
However, the Scriptures don't really deal with or show a woman divorcing her husband.
Paul relates to us that such a scenario isn't permitted according to the Torah:
Romans 7:1-3 (ESV),
The same Paul, however, wrote this:
1 Corinthians 7:12-16 (ESV),
First, please note that Paul admits to not writing this portion under divine inspiration, but rather, is giving good pastoral wisdom and advice. Second, notice what Paul writes about the unbelieving spouse; if he or she separates (departs in the KJV), let it be so. Meaning what?
Meaning there is no spiritually binding and divine moral obligation on the behalf of the faithful, believing spouse, to reconcile and make the marriage work.
If the unbeliever leaves, the believer is free to close the door on that marriage, whether the believer is a man or a woman.
I would argue that a cheating spouse who leaves a marriage to go whoring after someone else, is by definition, an unbeliever. Such a scenario frees the innocent party from being "enslaved", meaning bound to the oath and covenant of the marriage.
Divorce may then proceed, according to both Paul's teachings and the Torah. And if a divorce occurs, the offending party may indeed marry again.
The question then becomes, but did God join the offending party to the second spouse? Not necessarily. When Christ taught on this, He said "What...God has joined together, let not man separate" (See
Matthew 19:6 and
Mark 10:9).
There, the word for "separate" is the same as used by Paul in
1 Corinthians 7.
So, it might indicate that no one on earth has the right to separate two people who have been married. But, Paul makes the case that an unbeliever may leave, and the believer is then free. So, is Paul disagreeing with Jesus?
I don't think so. In both
Matthew 19:6 and
Mark 10:9, "man" is anarthrous, meaning it contains no article before it. This makes "man" a generic reference to humanity. Christ's context is less about specific individual cases of marriage, but rather, about marriage as an institution.
Now, in Mark, we only read that Jesus stipulates the following:
Mark 10:10-12 (ESV),
This would seem Jesus doesn't permit divorce and subsequent marriage under any circumstances. But Matthew clarifies:
Matthew 19:9 (ESV),
Note that Jesus doesn't expound on which of the two parties in a marriage is guilty of sexual immorality. The man may divorce his wife because of his own sexual immorality! If he cheats on her, and they divorce, and then marries another, even if he goes on to marry the woman with whom he had an affair, the exception clause goes into effect.
The sexual immorality clause has been triggered, the marriage can be rendered over, divorce may ensue, and marriage by either the offending or innocent party may take place.