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On *-bimultipliers, Generalized *-biderivations and Related Mappings

Ali, Shakir;Khan, Mohammad Salahuddin

  • Received : 2010.07.22
  • Accepted : 2011.04.06
  • Published : 2011.09.23

Abstract

In this paper we dene the notions of left *-bimultiplier, *-bimultiplier and generalized *-biderivation, and to prove that if a semiprime *-ring admits a left *-bimultiplier M, then M maps R ${\times}$ R into Z(R). In Section 3, we discuss the applications of theory of *-bimultipliers. Further, it was shown that if a semiprime *-ring R admits a symmetric generalized *-biderivation G : R ${\times}$ R ${\rightarrow}$ R with an associated nonzero symmetric *-biderivation R ${\times}$ R ${\rightarrow}$ R, then G maps R ${\times}$ R into Z(R). As an application, we establish corresponding results in the setting of $C^*$-algebra.

Keywords

Prime(semiprime) *-ring;$C^*$-algebra;left *-bimultiplier;*-bimultiplier;generalized *-biderivation;generalized reverse *-biderivation

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  1. On Jordan ∗-mappings in rings with involution vol.24, pp.1, 2016, https://doi.org/10.1016/j.joems.2014.12.006
  2. GENERALIZED (α, β)*-DERIVATIONS AND RELATED MAPPINGS IN SEMIPRIME *-RINGS vol.05, pp.02, 2012, https://doi.org/10.1142/S1793557112500155