izvuzmathИзвестия высших учебных заведений. МатематикаIzvestiya Vysshikh Uchebnykh Zavedenii. Matematika0021-34462076-4626Казанский (Приволжский) федеральный университет10.26907/0021-3446-2026-7-66-79izvuzmath-322Research ArticleСтатьиОб общих свойствах элементов в кольце и их приложенияхOn common properties of elements in a ring and their applicationsХаджиС.HadjiS.

Суфиан Хаджи

Рабат, а/я 5118, 10105

Soufiane Hadji

B. P. 5118, Rabat, 10105

soufiane.hadji@usmba.ac.maЗгуиттиХ.ZguittiH.

Хассан Згуитти

Фес, 30003

Hassane Zguitti

Fez, 30003

zguitti@usmba.ac.maРабатский университет Мохаммеда VМароккоMohammed V University in RabatMoroccoУниверситет Сиди Мохаммеда Бен АбдаллахМароккоSidi Mohamed Ben Abdellah UniversityMorocco202606082026076679Copyright © Хаджи С., Згуитти Х., 20262026Хаджи С., Згуитти Х.Hadji S., Zguitti H.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://izvuzmath.elpub.ru/jour/article/view/322

В ассоциативном кольце $\mathcal{R}$ с единичным элементом, обозначаемым как 1, даны два элемента $a$, $b\in \mathcal{R}$, удовлетворяющие уравнениям $a^{m+1}=b a^{m}$ и $b^{m+1}=ab^m$ для некоторого $m\geq 2$. В работе изучаются общие спектральные свойства обратимости элементов $1-a$ (соответственно, $a$) и $1-b$ (соответственно, $b$) сильно по Дразину, обобщенно сильно по Дразину, по Хирано и обобщенно по Хирано. Рассмотрено применение полученных результатов к $\nu$-сходимости в банаховой алгебре.

In an associative ring $\mathcal{R}$ with a unit element denoted by 1, given two elements $a$ and $b\in \mathcal{R}$ satisfying the equations $a^{m+1}=b a^{m} \mbox{ and } b^{m+1}=ab^m\ \mbox{ for some }m\geq 2$. We study common spectral properties for (strong Drazin, generalized strong Drazin, Hirano, generalized Hirano) invertibility of $1-a$ (respectively, $a$) and $1-b$ (respectively, $b$). An application of the obtained results to the $\nu$-convergence in a Banach algebra is given.

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The authors declare that there are no conflicts of interest present.