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Abstrakty
Let R be a 2-torsion free semiprime ring equipped with an involution *. An additive mapping T : R → R is called a left (resp. right) Jordan α-* centralizer associated with a function α : R → R if T(x2) = T(x)α(x*) (resp. T(x2) = α(x*)T(x)) holds for all x (…) R. If T is both left and right Jordan α-* centralizer of R, then it is called Jordan α-* centralizer of R. In the present paper it is shown that if α is an automorphism of R, and T : R → R is an additive mapping such that 2T(xyx) = T(x)α(y*x*) + α(x*y*)T(x) holds for all x; y (…) R, then T is a Jordan α-* centralizer of R.
Wydawca
Czasopismo
Rocznik
Tom
Strony
130--136
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
autor
- Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
autor
- Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Bibliografia
- [1] E. Albas, On τ-centralizers of semiprime rings, Siberian Math. J. 48(2) (2007), 191–196.
- [2] M. N. Daif, M. S. El-Sayiad, On generalized derivations of semiprime rings with involuation, Internat. J. Algebra 1(12) (2007), 551–555.
- [3] M. N. Daif, M. S. El-Sayiad, On Jordan and Jordan *-generalized derivations in semiprime rings with involution, Int. J. Contemp. Math. Sciences 2(30) (2007), 1487–1492.
- [4] M. N. Daif, M. S. El-Sayiad, N. M. Muthana, An identity on θ-centralizers of semiprime rings, Int. Math. Forum 3(19) (2008), 937–944.
- [5] L. Molnar, On centralizers of an H*-algebra, Publ. Math. Debrecen 46(1–2) (1995), 89–95.
- [6] J. Vukman, An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolin. 40(3) (1999), 447–456.
- [7] J. Vukman, Centralizers on semiprime rings, Comment. Math. Univ. Carolin. 42(2) (2001), 237–245.
- [8] J. Vukman, I. K. Ulbl, On centralizers of semiprime rings, Aequationes Math. 66 (2003), 277–283.
- [9] J. Vukman, I. K. Ulbl, On centralizers of semiprime rings with involution, Studia Sci. Math. Hungar. 43(1) (2006), 61–67.
- [10] J. Vukman, A note on generalized derivations of semiprime rings, Taiwanese J. Math. 11(2) (2007), 367–370.
- [11] B. Zalar, On centralizers of semiprime rings, Comment. Math. Univ. Carolin. 32 (1991), 609–614.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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