What is the ruling regarding a man swearing "By divorce, I will not sleep with you for a week" with the intention of not having intercourse with his wife, and does his oath take effect if she sleeps next to him or he kisses her, despite his clear intention not to have intercourse?

The fatwa regarding an oath sworn by divorce is that divorce occurs if the oath is broken, whether the swearer intended to effect a divorce or intended to threaten, confirm, or prevent. Some scholars, such as Ibn Taymiyyah, are of the view that an oath not intended to effect a divorce has the same ruling as an oath sworn by Allah, requiring an expiation for an oath (kaffarat yamin) and not resulting in divorce.

The ruling here, based on what is considered authoritative, is that divorce occurs when the oath is broken. Breaking the oath only occurs by engaging in sexual intercourse with the wife before the week ends. As for merely sleeping with her or enjoying her without intercourse, this does not break the oath as long as the swearer's intention was to refrain from sexual intercourse, because the consideration in an oath is the intention of the swearer.

The permissible oath is to swear by Allah the Almighty. As for swearing by divorce, it is an oath of the wicked and can lead to dire consequences.