Does the Prophetic hadith: "There is no prayer for one who has no ablution, and there is no ablution for one who has not mentioned the name of Allah upon it" mean that the ablution, and consequently the prayer, is invalid for one who has not mentioned the name of Allah upon it? And if so, what is the ruling concerning past prayers that were performed without uttering the Basmala during ablution?

The meaning of the hadith (definition), "There is no ablution for one who does not mention the name of Allah upon it," is not to be taken literally. Rather, it refers to one who performs ablution or ghusl (definition) without the intention of prayer or purifying from major ritual impurity. Other narrations state that whoever performs ablution and mentions the name of Allah, their entire body becomes purified, whereas whoever does not mention the name of Allah, only the washed parts of the body become purified. Scholars have differed regarding mentioning Allah's name (Tasmiyah) during ablution: the majority of scholars hold that it is desirable (mustahabb) but not obligatory, and its omission does not harm, whether by forgetfulness or intentionally, and the ablution is valid without it. However, Imam Ahmad holds that mentioning Allah's name is obligatory at the beginning of ablution, and intentionally omitting it invalidates the purification. The preponderant opinion is that of the majority of scholars.