Nonlinear skew commuting maps on -rings

Authors

  • L. Kong School Math. and Statistics, Shaanxi Normal Univ., and Inst. Appl. Math., Shangluo Univ., China
  • J. Zhang School Math. and Statistics, Shaanxi Normal Univ., China

DOI:

https://doi.org/10.37863/umzh.v74i6.801

Keywords:

Commuting maps; skew commuting maps; rings

Abstract

UDC 512.5

Let R be a unital -ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP=0 implies A=0 and AR(IP)=0 implies A=0. In this paper, it is proved that if ϕ:RR is a nonlinear skew commuting map, then there exists an element ZZS(R) such that ϕ(X)=ZX for all XR, where ZS(R) is the symmetric center of R.
As an application, the form of nonlinear skew commuting maps on factors is obtained.

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Published

07.07.2022

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Section

Research articles

How to Cite

Kong, L., and J. Zhang. “Nonlinear Skew Commuting Maps on -Rings”. Ukrains’kyi Matematychnyi Zhurnal, vol. 74, no. 6, July 2022, pp. 826-31, https://doi.org/10.37863/umzh.v74i6.801.