## On certain pairs of functions of semiprime rings

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- by Matej Brešar
- Proc. Amer. Math. Soc.
**120**(1994), 709-713 - DOI: https://doi.org/10.1090/S0002-9939-1994-1181158-3
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## Abstract:

Let $f$ and $g$ be functions of a set $S$ into a semiprime ring $R$. A necessary and sufficient condition for $f$ and $g$ to satisfy $f(s)xg(t) = g(s)xf(t)$ for all $s,t \in S,x \in R$ is given. As an application, biderivations and commuting additive mappings of semiprime rings are characterized.## References

- S. A. Amitsur,
*Generalized polynomial identities and pivotal monomials*, Trans. Amer. Math. Soc.**114**(1965), 210–226. MR**172902**, DOI 10.1090/S0002-9947-1965-0172902-9
—, - W. E. Baxter and W. S. Martindale III,
*Jordan homomorphisms of semiprime rings*, J. Algebra**56**(1979), no. 2, 457–471. MR**528587**, DOI 10.1016/0021-8693(79)90349-1 - Matej Brešar,
*Semiderivations of prime rings*, Proc. Amer. Math. Soc.**108**(1990), no. 4, 859–860. MR**1007488**, DOI 10.1090/S0002-9939-1990-1007488-X - Matej Brešar,
*Centralizing mappings on von Neumann algebras*, Proc. Amer. Math. Soc.**111**(1991), no. 2, 501–510. MR**1028283**, DOI 10.1090/S0002-9939-1991-1028283-2 - Matej Brešar,
*Centralizing mappings and derivations in prime rings*, J. Algebra**156**(1993), no. 2, 385–394. MR**1216475**, DOI 10.1006/jabr.1993.1080 - Matej Brešar,
*Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings*, Trans. Amer. Math. Soc.**335**(1993), no. 2, 525–546. MR**1069746**, DOI 10.1090/S0002-9947-1993-1069746-X
M. Brešar, W. S. Martindale, and C. R. Miers, - Chen-Lian Chuang,
*On the structure of semiderivations in prime rings*, Proc. Amer. Math. Soc.**108**(1990), no. 4, 867–869. MR**1002154**, DOI 10.1090/S0002-9939-1990-1002154-9 - Wallace S. Martindale III,
*Prime rings satisfying a generalized polynomial identity*, J. Algebra**12**(1969), 576–584. MR**238897**, DOI 10.1016/0021-8693(69)90029-5 - Edward C. Posner,
*Derivations in prime rings*, Proc. Amer. Math. Soc.**8**(1957), 1093–1100. MR**95863**, DOI 10.1090/S0002-9939-1957-0095863-0

*On rings of quotients*, Sympos. Math.

**8**(1972), 149-164. P. Ara, private communication, 1991. P. Ara and M. Mathieu,

*An application of local multipliers to centralizing mappings of*${C^{\ast }}$-

*algebras*, preprint.

*Centralizing maps in prime rings with involution*, J. Algebra (to appear).

## Bibliographic Information

- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**120**(1994), 709-713 - MSC: Primary 16N60; Secondary 16W25
- DOI: https://doi.org/10.1090/S0002-9939-1994-1181158-3
- MathSciNet review: 1181158