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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.20 No.4

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THE RANGE INCLUSION RESULTS FOR ALGEBRAIC NIL DERIVATIONS ON COMMUTATIVE AND NONCOMMUTATIVE ALGEBRAS

THE RANGE INCLUSION RESULTS FOR ALGEBRAIC NIL DERIVATIONS ON COMMUTATIVE AND NONCOMMUTATIVE ALGEBRAS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2013, v.20 no.4, pp.243-249
https://doi.org/10.7468/jksmeb.2013.20.4.243
Toumi, Mohamed Ali (Departement des Mathematiques, Faculte des Sciences de Bizerte)
Toumi, Mohamed Ali. (2013). THE RANGE INCLUSION RESULTS FOR ALGEBRAIC NIL DERIVATIONS ON COMMUTATIVE AND NONCOMMUTATIVE ALGEBRAS, 20(4), 243-249, https://doi.org/10.7468/jksmeb.2013.20.4.243

Abstract

Let A be an algebra and D a derivation of A. Then D is called algebraic nil if for any $x{\in}A$ there is a positive integer n = n(x) such that $D^{n(x)}(P(x))=0$, for all $P{\in}\mathbb{C}[X]$ (by convention $D^{n(x)}({\alpha})=0$, for all ${\alpha}{\in}\mathbb{C}$). In this paper, we show that any algebraic nil derivation (possibly unbounded) on a commutative complex algebra A maps into N(A), where N(A) denotes the set of all nilpotent elements of A. As an application, we deduce that any nilpotent derivation on a commutative complex algebra A maps into N(A), Finally, we deduce two noncommutative versions of algebraic nil derivations inclusion range.

keywords
algebraic nil derivation, d-algebra, nilpotent derivation

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한국수학교육학회지시리즈B:순수및응용수학

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