본문 바로가기
KERD
논문KCI 등재

$b$-Generalized derivations on Banach algebras

Husain Alhazmi
대한수학회 (The Korean Mathematical Society)|2022.01|대한수학회논문집 (Communications of the KMS)|제37권 제1호|pp. 57-64|DOI 10.4134/CKMS.c200480

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Banach algebra$b$-generalized derivationright Martindale quotient ring
주제분류수학

초록

In this paper, we show, among others, that if $A$ is a Banach algebra satisfying a functional identity involving a $b$-generalized derivation $F$ on $A$, under some mild conditions, is of the form $F(x)=ax$ for all $x\in R$, where $a\in Q_r$, a right Martindale quotient ring of $A$.

Abstract

In this paper, we show, among others, that if $A$ is a Banach algebra satisfying a functional identity involving a $b$-generalized derivation $F$ on $A$, under some mild conditions, is of the form $F(x)=ax$ for all $x\in R$, where $a\in Q_r$, a right Martindale quotient ring of $A$.

참고문헌 (17)

  1. SHAKIR ALI, "ON COMMUTATIVITY OF BANACH ALGEBRAS WITH DERIVATIONS", Bulletin of the Australian Mathematical Society, 91(3), pp.419~425 (2015), Cambridge University Press (CUP)[DOI]
  2. Mohammad Ashraf, "On commutativity of rings and Banach algebras with generalized derivations", Advances in Pure and Applied Mathematics, 10(2), pp.155~163 (2019), ISTE Group[DOI]
  3. Howard E. Bell, "On a commutativity theorem of Herstein", Archiv der Mathematik, 21(1), pp.265~267 (1970), Springer Science and Business Media LLC[DOI]
  4. Howard E. Bell, "ON THE COMMUTATIVITY OF PRIME RINGS WITH DERIVATION", Quaestiones Mathematicae, 22(3), pp.329~335 (1999), Informa UK Limited[DOI]
  5. I. N. Herstein, "Power maps in rings", Michigan Math. J, 8, pp.29~32 (1961)
  6. I. N. Herstein, "A remark on rings and algebras", Michigan Math. J, 10, pp.269~272 (1963)
  7. Abdul Nadim Khan, "On skew derivations and generalized skew derivations in Banach algebras", Quaestiones Mathematicae, 43(9), pp.1259~1272 (2019), National Inquiry Services Center (NISC)[DOI]
  8. M. TAMER KOŞAN, "<i>b<", i>-GENERALIZED DERIVATIONS OF SEMIPRIME RINGS HAVING NILPOTENT VALUES, 2014, pp.96(3), 326~337[DOI]
  9. E. C. Posner, "Derivations in prime rings", Proc. Amer. Math. Soc, 8, pp.1093~1100 (1957)[DOI]
  10. B. Prajapati, "Some commutativity theorems on Banach algebras", Rendiconti del Circolo Matematico di Palermo Series 2, 70(2), pp.1041~1049 (2020), Springer Science and Business Media LLC[DOI]
  11. Nadeem ur Rehman, "On continuous linear generalized derivation in rings and Banach algebras", Asian-European Journal of Mathematics, 14(02), pp.2150020~ (2019), World Scientific Pub Co Pte Lt[DOI]
  12. G. S. Sandhu, "On derivations satisfying certain identities on rings and algebras", Facta Univ. Ser. Math. Inform, 34(1), pp.85~99 (2019)
  13. R. K. Sharma, "Generalized derivations and commutativity of prime Banach algebras", Beiträge zur Algebra und Geometrie, 2016, pp.58(1), 179~187[DOI]
  14. J. Vukman, "Commuting and centralizing mappings in prime rings", Proc. Amer. Math. Soc, 109(1), pp.47~52 (1990)[DOI]
  15. J. Vukman, "A result concerning derivations in noncommutative Banach algebras", Glas. Mat. Ser. III, 26(1-2), pp.83~88 (1991)
  16. J. Vukman, "On derivations in prime rings and Banach algebras", Proc. Amer. Math. Soc, 116(4), pp.877~884 (1992)[DOI]
  17. Bertram Yood, "On Commutativity of Unital Banach Algebras", Bulletin of the London Mathematical Society, 23(3), pp.278~280 (1991), Wiley[DOI]

관련 논문AI추천

On generalized derivations in rings and Banach algebrasAbderrahman Hermas, Karim Bouchannafa, Lahcen Oukhtite장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2024 · 제27권 제2호Generalized derivations in prime rings and noncommutative Banach algebrasVincenzo De Filippis대한수학회 · 대한수학회보2008 · 제45권 제4호The properties of Jordan derivations of semiprime rings and Banach algebras, IIByung Do Kim대한수학회 · 대한수학회논문집2019 · 제34권 제3호A REMARK ON GENERALIZED DERIVATIONS IN RINGS AND ALGEBRASNadeem Ur Rehman한국수학교육학회 · 이론수학과 교직수학2018 · 제25권 제3호Derivations 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 제2호Pair of (generalized-)derivations on rings and Banach algebrasFeng Wei, Zhankui Xiao대한수학회 · 대한수학회보2009 · 제46권 제5호

이 간행물의 다른 논문 (22건)

Decompositions of graded maximal submodulesFida Moh’Dpp. 1-15When is $C(X)$ an EM-ring?Isaaf Atassi, Emad Abu Osbapp. 17-29A note on modular equations of signature 2 and their evaluationsSHRUTHI, Arjun Kumar Rathie, Belakavadi Radhakrishna Srivatsa Kumar, Nagara Vinayaka Udupa Sayinathpp. 31-43Rings in which every ideal contained in the set of zero-divisors is a d-idealNajib Mahdou, Abdeslam Mimouni, Adam Anebripp. 45-56A note on defectless extensions of henselian valued fieldsAzadeh Niksereshtpp. 65-74
원문 보기