Centralizers on prime and semiprime rings
Vukman, Joso
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 231-240 / Harvested from Czech Digital Mathematics Library
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The purpose of this paper is to investigate identities satisfied by centralizers on prime and semiprime rings. We prove the following result: Let $R$ be a noncommutative prime ring of characteristic different from two and let $S$ and $T$ be left centralizers on $R$. Suppose that $[S(x),T(x)]S(x)+S(x)[S(x),T(x)]=0$ is fulfilled for all $x\in R$. If $S\neq 0$ $(T\neq 0)$ then there exists $\lambda $ from the extended centroid of $R$ such that $T=\lambda S$ $(S=\lambda T)$.

Publié le : 1997-01-01
Classification:  16A12,  16A68,  16A72,  16N60,  16U70,  16W10,  16W25 
@article{118920,
     author = {Joso Vukman},
     title = {Centralizers on prime and semiprime rings},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {231-240},
     zbl = {0889.16016},
     mrnumber = {1455489},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118920}
}

Vukman, Joso. Centralizers on prime and semiprime rings. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 231-240. http://gdmltest.u-ga.fr/item/118920/

Brešar M.; Vukman J. Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-323. (1988) | MR 0943433

Brešar M. Jordan derivations on prime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006. (1988) | MR 0929422

Brešar M. On a generalization of the notion of centralizing mappings, Proc. Amer. Math. Soc. 114 (1992), 641-649. (1992) | MR 1072330

Brešar M. Centralizing mappings and derivations in prime rings, Journal of Algebra 156 (1993), 385-394. (1993) | MR 1216475

Brešar M. Commuting traces of biaditive mappings, commutativity-preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335 (1993), 525-545. (1993) | MR 1069746

Cusak J. Jordan derivations on rings, Proc. Amer. Math. Soc. 53 (1975), 321-324. (1975) | MR 0399182

Herstein I.N. Jordan derivations on prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110. (1957) | MR 0095864

Herstein I.N. Rings with involution, Univ. of Chicago Press, Chicago, 1976. | MR 0442017 | Zbl 0495.16007

Martindale W.S. Prime rings satisfying a generalized polynomial identity, Journal of Algebra 12 (1969), 576-584. (1969) | MR 0238897 | Zbl 0175.03102

Posner E. Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100. (1957) | MR 0095863

Zalar B. On centralizers of semiprime rings, Comment. Math. Univ. Carolinae 32 (1991), 609-614. (1991) | MR 1159807 | Zbl 0746.16011