Fully idempotent rings have regular centroids
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- by R. C. Courter PDF
- Proc. Amer. Math. Soc. 43 (1974), 293-296 Request permission
Abstract:
We prove that the centroid of a ring all of whose ideals are idempotent is commutative and regular in the sense of von Neumann. The center of a fully idempotent ring is regular. Evidently every regular ring is fully idempotent. One nonregular example is Sasiada’s simple radical ring. A subring of the countably infinite row-finite matrices over Sasiada’s ring provides an example of a nonsimple, indecomposable, nonregular fully idempotent ring.References
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- E. Sąsiada, Solution of the problem of existence of simple radical ring, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 9 (1961), 257 (English, with Russian summary). MR 125860
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 293-296
- MSC: Primary 16A32
- DOI: https://doi.org/10.1090/S0002-9939-1974-0330217-0
- MathSciNet review: 0330217