ON FULLY IDEMPOTENT RINGS

Title & Authors
ON FULLY IDEMPOTENT RINGS
Jeon, Young-Cheol; Kim, Nam-Kyun; Lee, Yang;

Abstract
We continue the study of fully idempotent rings initiated by Courter. It is shown that a (semi)prime ring, but not fully idempotent, can be always constructed from any (semi)prime ring. It is shown that the full idempotence is both Morita invariant and a hereditary radical property, obtaining $\small{hs(Mat_n(R))\;=\;Mat_n(hs(R))}$ for any ring R where hs(-) means the sum of all fully idempotent ideals. A non-semiprimitive fully idempotent ring with identity is constructed from the Smoktunowicz's simple nil ring. It is proved that the full idempotence is preserved by the classical quotient rings. More properties of fully idempotent rings are examined and necessary examples are found or constructed in the process.
Keywords
fully idempotent ring;(weakly) regular ring;hereditary radical;classical quotient ring;
Language
English
Cited by
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