Prime rings with involution involving left multipliers

• Boua, Abdelkarim ^[2] ; Ashraf, Mohammed ^[1]
  1. [1] Aligarh Muslim University

     Aligarh Muslim University

     India

     
  2. [2] Sidi Mohammed Ben Abdellah University.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 2, 2020, págs. 341-359
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-02-0021
• Enlaces
  • Texto completo
• Resumen

  • Let R be a prime ring of characteristic different from 2 with involution ’∗’ of the second kind and n ≥ 1 be a fixed positive integer. In the present paper it is shown that if R admits nonzero left multipliers S and T, then the following conditions are equivalent: (i) R is commutative. (ii) Tn([x, x∗]) 2 Z(R) for all x 2 R; (iii) Tn(x ◦ x∗) 2 Z(R) for all x 2 R; (iv) [S(x), T(x∗)] 2 Z(R) for all x 2 R; (v) [S(x), T(x∗)] - (x ◦ x∗) 2 Z(R) for all x 2 R; (vi) S(x) ◦ T(x∗) 2 Z(R) for all x 2 R; (vii) S(x) ◦ T(x∗) - [x, x∗] 2 Z(R) for all x 2 R. The existence of hypotheses in various theorems have been justified by the examples.

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