Об общих свойствах элементов в кольце и их приложениях

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.

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