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CERTAIN DIFFERENTIAL IDENTITIES INVOLVING SKEW LIE PRODUCT AND GENERALIZED DERIVATIONS

Md. Arshad Mmadni|Mohd Shadab Khan|Muzibur Rahman Mozumder
장전수학회 (Jangjeon Mathematical Society)|2024.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제27권 제2호|pp. 383-392|DOI 10.17777/pjms.2024.27.2.023

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키워드

derivationη-Prime ringinvolutiongeneralized derivationskew Lie product
주제분류수학

초록

Let ℜ be a ring with involution η. Notation ∇[ℓ₁, ℓ₂] is called skew-Lie product and defined by ℓ₁ℓ₂ − ℓ₂η(ℓ₁). The main objective of this paper is to investigate commutativity of η-prime rings with involution η of the second kind equipped with skew-Lie product involving a generalized derivation. Finally, we furnish some examples which illustrate that the requirements presumed in our results are not redundant.

Abstract

Let ℜ be a ring with involution η. Notation ∇[ℓ₁, ℓ₂] is called skew-Lie product and defined by ℓ₁ℓ₂ − ℓ₂η(ℓ₁). The main objective of this paper is to investigate commutativity of η-prime rings with involution η of the second kind equipped with skew-Lie product involving a generalized derivation. Finally, we furnish some examples which illustrate that the requirements presumed in our results are not redundant.

참고문헌 (18)

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관련 논문AI추천

Study of Generalized Derivations in Rings with InvolutionAdnan Abbasi, Muzibur Rahman Mozumder, Nadeem Ahmad Dar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2019 · 제59권 제1호On n-skew Lie Products on Prime Rings with InvolutionMohammad Salahuddin Khan, Muzibur Rahman Mozumder, Shakir Ali경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2022 · 제62권 제1호A study of differential identities on $\sigma$-prime ringsAdnan Abbasi, Md. Arshad Madni, Muzibur Rahman Mozumder대한수학회 · 대한수학회논문집2023 · 제38권 제3호Generalized derivations in ring with involution involving symmetric and skew symmetric elementsAbdellah Mamouni, Hajar El Mir, Souad Dakir대한수학회 · 대한수학회논문집2024 · 제39권 제1호ON η−GENERALIZED DERIVATIONS IN RINGS WITH JORDAN INVOLUTIONPhool Miyan대한수학회 · 대한수학회논문집2024 · 제39권 제3호Commutators and anti-commutators having automorphisms on Lie ideals in prime ringsHussain Alhazmi, Mohd Arif Raza강원경기수학회 · 한국수학논문집2020 · 제28권 제3호

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