# Centralizers on prime and semiprime rings

Commentationes Mathematicae Universitatis Carolinae (1997)

- Volume: 38, Issue: 2, page 231-240
- ISSN: 0010-2628

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topVukman, Joso. "Centralizers on prime and semiprime rings." Commentationes Mathematicae Universitatis Carolinae 38.2 (1997): 231-240. <http://eudml.org/doc/248087>.

@article{Vukman1997,

abstract = {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\ne 0$$(T\ne 0)$ then there exists $\lambda $ from the extended centroid of $R$ such that $T=\lambda S$$(S=\lambda T)$.},

author = {Vukman, Joso},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {prime ring; semiprime ring; extended centroid; derivation; Jordan derivation; left (right) centralizer; Jordan left (right) centralizer; commuting mapping; centralizing mapping; prime rings; semiprime rings; extended centroids; derivations; Jordan derivations; left centralizers; Jordan right centralizers; commuting mappings; centralizing mappings},

language = {eng},

number = {2},

pages = {231-240},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Centralizers on prime and semiprime rings},

url = {http://eudml.org/doc/248087},

volume = {38},

year = {1997},

}

TY - JOUR

AU - Vukman, Joso

TI - Centralizers on prime and semiprime rings

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1997

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 38

IS - 2

SP - 231

EP - 240

AB - 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\ne 0$$(T\ne 0)$ then there exists $\lambda $ from the extended centroid of $R$ such that $T=\lambda S$$(S=\lambda T)$.

LA - eng

KW - prime ring; semiprime ring; extended centroid; derivation; Jordan derivation; left (right) centralizer; Jordan left (right) centralizer; commuting mapping; centralizing mapping; prime rings; semiprime rings; extended centroids; derivations; Jordan derivations; left centralizers; Jordan right centralizers; commuting mappings; centralizing mappings

UR - http://eudml.org/doc/248087

ER -

## References

top- Brešar M., Vukman J., Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-323. (1988) MR0943433
- Brešar M., Jordan derivations on prime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006. (1988) MR0929422
- Brešar M., On a generalization of the notion of centralizing mappings, Proc. Amer. Math. Soc. 114 (1992), 641-649. (1992) MR1072330
- Brešar M., Centralizing mappings and derivations in prime rings, Journal of Algebra 156 (1993), 385-394. (1993) MR1216475
- Brešar M., Commuting traces of biaditive mappings, commutativity-preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335 (1993), 525-545. (1993) MR1069746
- Cusak J., Jordan derivations on rings, Proc. Amer. Math. Soc. 53 (1975), 321-324. (1975) MR0399182
- Herstein I.N., Jordan derivations on prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110. (1957) MR0095864
- Herstein I.N., Rings with involution, Univ. of Chicago Press, Chicago, 1976. Zbl0495.16007MR0442017
- Martindale W.S., Prime rings satisfying a generalized polynomial identity, Journal of Algebra 12 (1969), 576-584. (1969) Zbl0175.03102MR0238897
- Posner E., Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100. (1957) MR0095863
- Zalar B., On centralizers of semiprime rings, Comment. Math. Univ. Carolinae 32 (1991), 609-614. (1991) Zbl0746.16011MR1159807

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