A Closed Formula of Hausdorff Series in a Semigroup Ring
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Tarih
2020
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Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Let ?? be a fileld of characteristic zero, ?? and ?? be algebraically independent variables and ?????,??? be the free associative noncommutative algebra of rank 2 over ??. Each element in ?????,??? can be written as a noncommutative polynomial of ?? and ??. The expression of the polynomial ??=??(??,??)=log (????????) is a formal power series and a solution to this equation for ?? is given by the Hausdorff series expressed as nested commutators of ?? and ??. However this series is not in its closed form in ?????,???. Obtaining a closed form of this series, one may consider another algebraic structure other than ?????,??? and evolute the series in it. We consider the right zero semigroup with finite elements, and the semigroup ring ?? spanned on this semigroup over the field of real numbers. In this paper, we provide a closed form of this formula in the semigroup ring ??.
Açıklama
Anahtar Kelimeler
Matematik
Kaynak
Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi
WoS Q Değeri
Scopus Q Değeri
Cilt
36
Sayı
3
