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JORDAN DERIVATIONS ON A LIE IDEAL OF A SEMIPRIME RING AND THEIR APPLICATIONS IN BANACH ALGEBRAS

김병도
한국수학교육학회|2016.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제23권 제4호|pp. 347-375

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참고문헌

키워드

derivationprime ringBanach algebrasemiprime ringLie idealJordan derivation(Jacobson) radical
주제분류수학

초록

Let R be a 3!-torsion free noncommutative semiprime ring, U a Lie ideal of R; and let D : R → R be a Jordan derivation. If [D(x), x]D(x) = 0 for all x ∈ U, then D(x)[D(x), x]y - yD(x)[D(x), x] = 0 for all x, y ∈ U. And also. if D(x)[D(x), x] = 0 for all x ∈ U, then [D(x), x]D(x)y - y[D(x), x]D(x) = 0 for all x, y ∈ U. And we shall give their applications in Banach algebras.

Abstract

Let R be a 3!-torsion free noncommutative semiprime ring, U a Lie ideal of R; and let D : R → R be a Jordan derivation. If [D(x), x]D(x) = 0 for all x ∈ U, then D(x)[D(x), x]y - yD(x)[D(x), x] = 0 for all x, y ∈ U. And also. if D(x)[D(x), x] = 0 for all x ∈ U, then [D(x), x]D(x)y - y[D(x), x]D(x) = 0 for all x, y ∈ U. And we shall give their applications in Banach algebras.

참고문헌 (16)

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관련 논문AI추천

The properties of Jordan derivations of semiprime rings and Banach algebras, I김병도대한수학회 · 대한수학회논문집2018 · 제33권 제1호JORDAN DERIVATIONS OF SEMIPRIME RINGS AND NONCOMMUTATIVE BANACH ALGEBRAS, I김병도한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제2호Derivations with Power Values on Lie Ideals in Rings and Banach AlgebrasMohd Arif Raza, Nadeem ur Rehman, Najat Mohammed Muthana경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호The properties of Jordan derivations of semiprime rings and Banach algebras, IIByung Do Kim대한수학회 · 대한수학회논문집2019 · 제34권 제3호Jordan Derivations of Semiprime Rings and Noncommutative Banach Algebras, II김병도한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제3호Pair of (generalized-)derivations on rings and Banach algebrasFeng Wei, Zhankui Xiao대한수학회 · 대한수학회보2009 · 제46권 제5호

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