DOI QR코드

DOI QR Code

ON GENERALIZED (α, β)-DERIVATIONS AND COMMUTATIVITY IN PRIME RINGS

  • Jung, Yong-Soo ;
  • Park, Kyoo-Hong
  • 발행 : 2006.02.01

초록

Let R be a prime ring and I a nonzero ideal of R. Let $\alpha,\;\nu,\;\tau\;R{\rightarrow}R$ be the endomorphisms and $\beta,\;\mu\;R{\rightarrow}R$ the automorphisms. If R admits a generalized $(\alpha,\;\beta)-derivation$ g associated with a nonzero $(\alpha,\;\beta)-derivation\;\delta$ such that $g([\mu(x),y])\;=\;[\nu/(x),y]\alpha,\;\tau$ for all x, y ${\in}I$, then R is commutative.

키워드

generalized $(\alpha,\;\beta)-derivation$;prime ring;commutativity

참고문헌

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피인용 문헌

  1. On rings with some kinds of centrally-extended maps vol.57, pp.3, 2016, https://doi.org/10.1007/s13366-015-0274-2
  2. On Generalized ()-Derivations in Semiprime Rings vol.2012, 2012, https://doi.org/10.5402/2012/120251