A backup of a deleted PSQ : https://math.stackexchange.com/q/3955443/290189
OP : irfanmat
It has a detailed answer by Atticus Stonestrom. It’s pity that his post got deleted. As there’s no reason for undeletion, I’m posting it here so as to preserve the contents.
Question body Is there a semi-simple and projective but not injective module? I will be glad if you help.
Response(s) In the non-commutative case, the answer is yes.