Geodesic
A decomposition theorem for semiprime rings
Algebra and discrete mathematics, no. 1 (2005), pp. 62-68

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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. 
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     author = {Marina Khibina},
     title = {A decomposition theorem for semiprime rings},
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     number = {1},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2005_1_a5/}
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Marina Khibina. A decomposition theorem for semiprime rings. Algebra and discrete mathematics, no. 1 (2005), pp. 62-68. http://geodesic.mathdoc.fr/item/ADM_2005_1_a5/