An identity related to \(\theta\)-centralizers in semiprime rings. (English) Zbl 1531.16014
Summary: Let \(R\) be a \(2\)-torsion-free semiprime ring and \(\theta\) be an epimorphism of \(R\). In this paper, under special hypotheses, we prove that if \(T(xyx)=\theta(x)T(y)\theta(x)\) holds for all \(x, y\in R\), then \(T\) is a \(\theta\)-centralizer.
References:
| [1] | 1. E. Albas, On τ-centralizers of semiprime rings, Sib. Math. J., 48(2) (2007), 191-196. · Zbl 1153.16028 |
| [2] | 2. M. N. Daif and M. S. Tammam El-Sayiad, On centralizers of semiprime rings (II), St. Petersburg Math. J., 21(1) (2010), 43-52. · Zbl 1196.16034 |
| [3] | 3. H. Gahramani, On centralizers of Banach algebras, Bull. Malays. Math. Sci. Soc., 38(1) (2015), 155-164. · Zbl 1341.47042 |
| [4] | 4. J. Vukman, An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolin., 40 (1999), 447-456. · Zbl 1014.16021 |
| [5] | 5. J. Vukman, Centralizers on semiprime rings, Comment. Math. Univ. Carolin., 42(2) (2001), 237-245. · Zbl 1057.16029 |
| [6] | 6. B. Zalar, On centralizers of semiprime rings, Comment. Math. Univ. Carolin., 32(4) (1991), 609-614. · Zbl 0746.16011 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
