Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON FULLY IDEMPOTENT RINGS

  • Jeon, Young-Cheol (DEPARTMENT OF MATHEMATICS KOREA SCIENCE ACADEMY) ;
  • Kim, Nam-Kyun (COLLEGE OF LIBERAL ARTS HANBAT NATIONAL UNIVERSITY) ;
  • Lee, Yang (DEPARTMENT OF MATHEMATICS EDUCATION BUSAN NATIONAL UNIVERSITY)
  • Received : 2010.09.29
  • Published : 2010.07.31
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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 $hs(Mat_n(R))\;=\;Mat_n(hs(R))$ 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

Acknowledgement

Supported by : National Research Foundation of Korea, Korea Research Foundation

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