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Thank you,but I do not know much about group theory.For the group algebra kG,we can induce a Lie structure by [a,b]=ab-ba naturelly,that is why I care about the Lie algebra over commutative ring.
“a ring R is von-Neumann regular ring iff every module over R is flat”，but Von-Neumann regular ring is also not artinian in general，so nonartin is not the reason.
