The additive group of commutative rings generated by idempotents-Reference-Cited by-同舟云学术

The additive group of commutative rings generated by idempotents

Published:1973 Issue:3 Volume:38 Page:499-502
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Hill Paul

Abstract

If R R is a ring, let R + {R^ + } denote its additive group. Our purpose is to give an elementary proof that if R R is a commutative ring generated by idempotents, then any subring of R R generated by idempotents is pure. This yields immediately an independent proof of the following result of G. M. Bergman. If R R is a commutative ring with identity and if R R is generated by idempotents, then R + {R^ + } is a direct sum of cyclic groups.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1973-038-03/S0002-9939-1973-0316439-2/S0002-9939-1973-0316439-2.pdf

Reference3 articles.

1. Boolean rings of projection maps;Bergman, George M.;J. London Math. Soc. (2),1972

2. Verallgemeinerung eines Satzes von Herrn E. Specker;Nöbeling, G.;Invent. Math.,1968

3. Additive Gruppen von Folgen ganzer Zahlen;Specker, Ernst;Portugal. Math.,1950

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