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The f regular Radicals of the Semirings with Reversible Addition

Chen Peici (Department of Mathematics,Jiangxi Normal University,Nanchang 330027)  
In this paper,we defined the f regular radicals of the semirings with reversible addition,and proved the structure theorems of the f regular semirings and the f regular semisimple semirings.Applying those results to the commutative rings,we gave the structure theorems of Von Neumann regular rings and Von Neumann regular semisimple rings,and new descriptions of the Jacobson radicals and the Jacobson semisimple rings.
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