We study the relationship between algebras generated by idempotents over a commutative ring $R$ with identity and algebras that are quotient rings of group algebras $RG$ for torsion abelian groups $G$ without an element whose order is a zero-divisor in $R$. The main purpose is to seek conditions for $R$ to hold the equality between these two kinds of algebras.
"Commutative rings over which algebras generated by idempotents are quotients of group algebras." J. Commut. Algebra 7 (3) 373 - 391, FALL 2015. https://doi.org/10.1216/JCA-2015-7-3-373