### Right Sided Ideals and Multilinear Polynomials with Derivation on Prime Rings

Basudeb Dhara, R. K. Sharma (2009)

Rendiconti del Seminario Matematico della Università di Padova

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Basudeb Dhara, R. K. Sharma (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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Janusz Zieliński (2002)

Colloquium Mathematicae

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We give a description of all local derivations (in the Kadison sense) in the polynomial ring in one variable in characteristic two. Moreover, we describe all local derivations in the power series ring in one variable in any characteristic.

De Filippis, Vincenzo (2005)

Mathematica Pannonica

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Nurcan Argaç, Vincenzo De Filippis, H. G. Inceboz (2008)

Rendiconti del Seminario Matematico della Università di Padova

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De Filippis, V., Di Vincenzo, O.M. (2001)

Mathematica Pannonica

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S.M. Bhatwadekar (1988/89)

Mathematische Zeitschrift

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De Filippis, Vincenzo (2004)

International Journal of Mathematics and Mathematical Sciences

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Roberto Dvornicich, Shih Ping Tung, Umberto Zannier (2003)

Acta Arithmetica

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De Filippis, V. (2006)

International Journal of Mathematics and Mathematical Sciences

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Amit Roy, Shrikant M. Bhatwadekar (1983)

Mathematische Zeitschrift

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Piotr Jędrzejewicz (2013)

Open Mathematics

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We obtain two equivalent conditions for m polynomials in n variables to form a p-basis of a ring of constants of some polynomial K-derivation, where K is a unique factorization domain of characteristic p > 0. One of these conditions involves Jacobians while the other some properties of factors. In the case m = n this extends the known theorem of Nousiainen, and we obtain a new formulation of the Jacobian conjecture in positive characteristic.