A Note on Posner s Theorem with Generalized Derivations on Lie Ideals
Vincenzo De Filippis, M. S. Tammam El-Sayiad (2009)
Rendiconti del Seminario Matematico della Università di Padova
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Vincenzo De Filippis, M. S. Tammam El-Sayiad (2009)
Rendiconti del Seminario Matematico della Università di Padova
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Leonid Makar-Limanov, Andrzej Nowicki (2001)
Colloquium Mathematicae
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Let k[[x,y]] be the formal power series ring in two variables over a field k of characteristic zero and let d be a nonzero derivation of k[[x,y]]. We prove that if Ker(d) ≠ k then Ker(d) = Ker(δ), where δ is a jacobian derivation of k[[x,y]]. Moreover, Ker(d) is of the form k[[h]] for some h ∈ k[[x,y]].
Nurcan Argaç, Vincenzo De Filippis, H. G. Inceboz (2008)
Rendiconti del Seminario Matematico della Università di Padova
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Michael G. Voskoglou (1994)
Publications de l'Institut Mathématique
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Krzysztof Jan Nowak (2010)
Annales Polonici Mathematici
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Given an algebraically closed field K of characteristic zero, we prove the Abhyankar-Jung theorem for any excellent henselian ring whose completion is a formal power series ring K[[z]]. In particular, examples include the local rings which form a Weierstrass system over the field K.
Michael Gr. Voskoglou (2004)
Acta Mathematica Universitatis Ostraviensis
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William F. Keigher (1981)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Chaudhry, Muhammad Anwar, Thaheem, A.B. (2004)
International Journal of Mathematics and Mathematical Sciences
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Basudeb Dhara, R. K. Sharma (2009)
Rendiconti del Seminario Matematico della Università di Padova
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Silvana Mauceri (1990)
Rendiconti del Seminario Matematico della Università di Padova
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Andrzej Nowicki (2002)
Banach Center Publications
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We present some facts, observations and remarks concerning the problem of finiteness of the rings of constants for derivations of polynomial rings over a commutative ring k containing the field ℚ of rational numbers.