On commutativity of rings with constraints involving a nil subset

• Abujabal, H. A. S. ^[1] ; Obaid, M. A. ^[1] ; Khan, M. A. ^[1]
  1. [1] King Abdul Aziz University Hospital

     King Abdul Aziz University Hospital

     Arabia Saudí

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 15, Nº. 1, 1996, págs. 91-99
• Idioma: inglés
• DOI: 10.22199/S07160917.1996.0001.00005
• Enlaces
  • Texto completo
• Resumen

  • The main theorem of this paper is that a ring R with unity is commutative if and only if there is a nil subset B of R such thatl. for each x ∊ R, either x ∊ Z(R) or there is a polynormial f over Z with x - x2 f (x)  ∊ B;2. for each x, y x ∊ R, there are non-negative integers n > 1, m, r, s depending on a pair of ring elements x,y with x(xmy ± xrynxs) - (xm y ± xrynxs)x = 0.A related result for a nil commutative subset of R is given and the restrictions on the hypothesis of our result are justified by examples.

• Referencias bibliográficas
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