RESEARCH ARTICLE

A decomposition theorem for semiprime rings

Marina Khibina

In-t of Engineering Thermophysics, NAS, Ukraine

Abstract: A ring $A$ is called an $FDI$-ring if there exists a decomposition of the identity of $A$ in a sum of finite number of pairwise orthogonal primitive idempotents. We call a primitive idempotent $e$ artinian if the ring $eAe$ is Artinian. We prove that every semiprime $FDI$-ring is a direct product of a semisimple Artinian ring and a semiprime $FDI$-ring whose identity decomposition doesn't contain artinian idempotents.

Keywords: minor of a ring, local idempotent, semiprime ring, Peirce decomposition.

MSC: 16P40, 16G10

Received: 27.09.2004
Revised: 21.03.2005

Language: English

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