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## PRIME RINGS WITH A FINITE NUMBER OF ALGEBRAIC ELEMENTS

Qiu Qizhang (Department of Mathematics, Wuhan University)
Let R be a ring. x∈R is called a algebraic element, if x~m+α_1x~(m-1)+……+a_(m-1)x=0 where α_i∈Z, i=1,2,……,m-1. Theoreml. Supposal R be a prime ring with a finite number of algebraic elements (≥2). (1)If R possesses zero divisors, then RM_n(F), the total matrix ring over field F of degree n, where n≥2, F=GF(p~m) (2)If R possesses no zero divisors, then (ⅰ) The set of all algebraic elements of R is a finite field GF(p~n) (ⅱ) R is the direct sum of the left GF(p~n) spaces R_0, R_1,……,R_(n_0), where n_0|n, R_i={x∈R|xa=a~(p~(i(n/n_0))x, Download(CAJ format) Download(PDF format)
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