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Rings in which every element is the sum of two idempotents

Published online by Cambridge University Press:  17 April 2009

Yasuyuki Hirano  and
Hisao Tominaga
Yasuyuki Hirano
Affiliation:
Department of Mathematics, Okayamna University, Okayama 700, Japan
Hisao Tominaga
Affiliation:
Department of Mathematics, Okayamna University, Okayama 700, Japan
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Abstract

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Let R be a ring with prime radical P. The main theorems of this paper are (1) The following conditions are equivalent.: 1) R is a commutative ring in which every element is the sum of two idempotents; 2) R is a ring in which every element is the sum of two commuting idempotents; 3) R satisfies the identity x3 = x. (2) If R is a PI-ring in which every element is the sum of two idempotents, then R/P satisfies the identity x3 = x. (3) Let R be a semi-perfect ring in which every element is the sum of two idempotents. If RRR is quasi-projective, then R is a finite direct sum of copies of GF(2) and/or GF(3).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 2 , April 1988 , pp. 161 - 164
Copyright
Copyright © Australian Mathematical Society 1988

References

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