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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Abstract

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

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

Dates
First available in Project Euclid: 14 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.jca/1450102161

Digital Object Identifier
doi:10.1216/JCA-2015-7-3-373

Mathematical Reviews number (MathSciNet)
MR3433988

Zentralblatt MATH identifier
1333.13008

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

Citation

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. https://projecteuclid.org/euclid.jca/1450102161


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