A note on periodic rings
Автор: Danchev Peter V.
Статья в выпуске: 4 т.23, 2021 года.
We obtain a new and non-trivial characterization of periodic rings (that are those rings R for which, for each element x in R, there exists two different integers m, n strictly greater than 1 with the property xm=xn) in terms of nilpotent elements which supplies recent results in this subject by Cui-Danchev published in (J. Algebra & Appl., 2020) and by Abyzov--Tapkin published in (J. Algebra & Appl., 2022). Concretely, we state and prove the slightly surprising fact that an arbitrary ring R is periodic if, and only if, for every element x from R, there are integers m>1 and n>1 with m≠n such that the difference xm-xn is a nilpotent.
Potent rings, periodic rings, nilpotent elements
Короткий адрес: https://readera.org/143177812
IDR: 143177812 | DOI: 10.46698/q0369-3594-2531-z
Список литературы A note on periodic rings
- Anderson, D. D. and Danchev, P. V. A Note on a Theorem of Jacobson Related to Periodic Rings, Proceedings of the American Mathematical Society, 2020, no. 12, vol. 148, pp. 5087-5089. DOI: 10.1090/proc/15246
- Cui, J. and Danchev, P. Some New Characterizations of Periodic Rings, Journal of Algebra and Its Applications, 2020, vol. 19, no. 12, 2050235. DOI: 10.1142/S0219498820502357
- Abyzov, A. N. and Tapkin, D. T. On Rings with xn-x Nilpotent, Journal of Algebra and Its Applications, 2022, vol. 21. DOI: 10.1142/S0219498822501110
- Abyzov, A. N., Danchev, P. V. and Tapkin, D. T. Rings with xn+x or xn-x Nilpotent, Journal of Algebra and Its Applications, 2023, vol. 22. DOI: 10.1142/S021949882350024X