On the symmetry of the Goldie and CS conditions for prime rings

Authors: Dinh Van Huynh, Đinh Văn Huỳnh, Sergio Lopez-Permouth, Jain Surender Kumar,

https://doi.org/10.1090/S0002-9939-00-05381-8

Publisher, magazine: ,

Publication year: 2000

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Abstract

It is shown that: (a) If R is a prime right Goldie right CS ring with right uniform dimension at least 2, then R is left Goldie, left CS; (b) A semiprime ring R is right Goldie left CS iff R is left Goldie, right CS.

Tags: right Goldie rings; right CS rings; prime rings; semiprime rings; direct summands; uniform dimensions

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On the symmetry of the Goldie and CS conditions for prime rings