Rings with idempotents in their nuclei-Reference-Cited by-同舟云学术

Rings with idempotents in their nuclei

Published:1975 Issue:0 Volume:208 Page:81-90
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Rich Michael

Abstract

Let R R be a prime nonassociative ring. If the set of idempotents of R R is a subset of the nucleus of R R or of the alternative nucleus of R R then it is shown that R R is respectively an associative or an alternative ring. Also if R R has one idempotent ≠ 0 , 1 \ne 0,1 which is in the Jordan nucleus or in the noncommutative Jordan nucleus then it is shown that R R is respectively a Jordan or a noncommutative Jordan ring.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1975-208-00/S0002-9947-1975-0371972-9/S0002-9947-1975-0371972-9.pdf

Reference10 articles.

1. Power-associative rings;Albert, A. A.;Trans. Amer. Math. Soc.,1948

2. A theory of power-associative commutative algebras;Albert, A. A.;Trans. Amer. Math. Soc.,1950

3. American Mathematical Society Colloquium Publications, Vol. 37;Jacobson, Nathan,1964

4. American Mathematical Society Colloquium Publications, Vol. XXXIX;Jacobson, Nathan,1968

5. Structure and representations of noncommutative Jordan algebras;McCrimmon, Kevin;Trans. Amer. Math. Soc.,1966

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