The additive group of commutative rings generated by idempotents
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- by Paul Hill PDF
- Proc. Amer. Math. Soc. 38 (1973), 499-502 Request permission
Abstract:
If $R$ is a ring, let ${R^ + }$ denote its additive group. Our purpose is to give an elementary proof that if $R$ is a commutative ring generated by idempotents, then any subring of $R$ generated by idempotents is pure. This yields immediately an independent proof of the following result of G. M. Bergman. If $R$ is a commutative ring with identity and if $R$ is generated by idempotents, then ${R^ + }$ is a direct sum of cyclic groups.References
- George M. Bergman, Boolean rings of projection maps, J. London Math. Soc. (2) 4 (1972), 593–598. MR 311531, DOI 10.1112/jlms/s2-4.4.593
- G. Nöbeling, Verallgemeinerung eines Satzes von Herrn E. Specker, Invent. Math. 6 (1968), 41–55 (German). MR 231907, DOI 10.1007/BF01389832
- Ernst Specker, Additive Gruppen von Folgen ganzer Zahlen, Portugal. Math. 9 (1950), 131–140 (German). MR 39719
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 499-502
- MSC: Primary 13A99
- DOI: https://doi.org/10.1090/S0002-9939-1973-0316439-2
- MathSciNet review: 0316439