ON NAKAYAMA'S EXTENSION OF THE x»<*> THEOREMS

@inproceedings{Rosenberg2010ONNE,
  title={ON NAKAYAMA'S EXTENSION OF THE x»<*> THEOREMS},
  author={Alex Rosenberg and DANIEL ZELINSKY and R In},
  year={2010}
}
where the a,are r fixed nonzero elements of Z, and 0<«i(a) <Ui(a) (i = 2, ■ ■ • , r), then A=Z. In [3, Theorem 11; 5; 2; l] specialized forms of (1) (e.g. cn(o) £Z, an(-a) —aEZ) are shown to imply commutativity at least for semi-simple rings. It is natural therefore to seek an extension of Nakayama's result to semi-simple rings. Since a semi-simple ring is a subdirect sum of primitive rings and (1) is preserved under homomorphism we first study primitive rings satisfying (1). If A is such a… CONTINUE READING

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