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Nilpotent elements of skew Hurwitz series rings. (English) Zbl 1353.16046

Summary: For a ring endomorphism \(\alpha\), we consider the problem of determining when an element \(f\) of the skew Hurwitz series ring \((HR,\alpha)\) is nilpotent. As an application, it is shown that the skew Hurwitz series ring \((HR,\alpha)\) is weak zip (resp. weak symmetric) if and only if \(R\) is weak zip (resp. weak symmetric) under some additional conditions. We also characterize when a skew Hurwitz series ring is 2-primal.

MSC:

16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras)
16S36 Ordinary and skew polynomial rings and semigroup rings
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