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

• Journal title : Kyungpook mathematical journal
• Volume 51, Issue 3,  2011, pp.301-309
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2011.51.3.301
Title & Authors
On *-bimultipliers, Generalized *-biderivations and Related Mappings

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 $\small{{\times}}$ 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 $\small{{\times}}$ R $\small{{\rightarrow}}$ R with an associated nonzero symmetric *-biderivation R $\small{{\times}}$ R $\small{{\rightarrow}}$ R, then G maps R $\small{{\times}}$ R into Z(R). As an application, we establish corresponding results in the setting of $\small{C^*}$-algebra.
Keywords
Prime(semiprime) *-ring;$\small{C^*}$-algebra;left *-bimultiplier;*-bimultiplier;generalized *-biderivation;generalized reverse *-biderivation;
Language
English
Cited by
1.
On Jordan ∗-mappings in rings with involution, Journal of the Egyptian Mathematical Society, 2016, 24, 1, 15
2.
GENERALIZED (α, β)*-DERIVATIONS AND RELATED MAPPINGS IN SEMIPRIME *-RINGS, Asian-European Journal of Mathematics, 2012, 05, 02, 1250015
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