He had no ambition for the caliphate
It is related that when on the way to Basra, Ali and his troops were camping at Rabdha, Ibn Abbas came to see him. At that time Ali was mending his shoe. Ali asked Ibn Abbas as to what would be the value of the shoe. Ibn Abbas said that the old shoe had hardly any value and its value would at the most not exceed a quarter of a dirham. Ali thereupon said, "By God, this shoe is more valuable to me than the caliphate. I have no ambition to rule."
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"When a person dies, his works end, except for three: ongoing charity, knowledge that is benefited from, and a righteous child who prays for him."
Prophet Mohammed (PBUH)
"The best of what a man leaves behind are three: a righteous child who supplicates for him, ongoing charity the reward of which reaches him, and knowledge that is acted upon after him."
Sunan Ibn Mājah
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Sahih Bukhari