Journal of Commutative Algebra

Commutative rings over which algebras generated by idempotents are quotients of group algebras

Hideyasu Kawai and Nobuharu Onoda

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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.

Article information

J. Commut. Algebra, Volume 7, Number 3 (2015), 373-391.

First available in Project Euclid: 14 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13A99: None of the above, but in this section
Secondary: 16S34: Group rings [See also 20C05, 20C07], Laurent polynomial rings


Kawai, Hideyasu; Onoda, Nobuharu. Commutative rings over which algebras generated by idempotents are quotients of group algebras. J. Commut. Algebra 7 (2015), no. 3, 373--391. doi:10.1216/JCA-2015-7-3-373.

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