What is the ruling on the fast of one who did not lower his gaze from forbidden things during the daytime in Ramadan, then slept and had a wet dream? And is the emission of semen in this case considered intentional, thereby invalidating his fast?

If one has a wet dream during the day in Ramadan (definition), their fast is valid, and they are not considered to have intentionally caused semen to be emitted if the wet dream occurred in their sleep. It is obligatory for a Muslim to lower their gaze from everything forbidden to look at, in compliance with the words of Allah Almighty: "Tell the believing men to reduce [some] of their gaze and guard their private parts. That is purer for them. Indeed, Allah is Acquainted with what they do" [An-Nur: 30], and this is particularly emphasized during the month of Ramadan.