Is fasting Ramadan generally also for the sake of Allah?

Fasting Ramadan (definition) is an obligation and a pillar of Islam. Every accountable Muslim who is not excused must complete its fast. Whoever fasts it out of faith and hope for reward will have their past sins forgiven. Scholars have differed on the meaning of "in the way of Allah" mentioned in the hadith (definition): "Whoever fasts a day in the way of Allah, Allah will distance his face from the Hellfire by seventy autumns." Some said it means obeying Allah with sincerity, while others said it means fasting while engaged in another act of worship, such as Hajj or Ghazw (military expedition). According to the first meaning, the fast of Ramadan is included, even though the hadith was narrated concerning supererogatory fasting.