On multiplicative (generalized)-$(\alpha,\beta)$-derivations in prime rings

UDC 512.5 We discuss some algebraic identities related to multiplicative (generalized)-derivations and multiplicative (generalized)-$(\alpha,\beta)$-derivations on appropriate subsets in prime rings.

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Date:2024
Main Authors: Garg, Chirag, Sharma, R. K.
Format: Article
Language:English
Published: Institute of Mathematics, NAS of Ukraine 2024
Online Access:https://umj.imath.kiev.ua/index.php/umj/article/view/654
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Journal Title:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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author Garg, Chirag
Sharma, R. K.
Garg, Chirag
Sharma, R. K.
author_facet Garg, Chirag
Sharma, R. K.
Garg, Chirag
Sharma, R. K.
author_sort Garg, Chirag
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datestamp_date 2024-06-19T00:35:09Z
description UDC 512.5 We discuss some algebraic identities related to multiplicative (generalized)-derivations and multiplicative (generalized)-$(\alpha,\beta)$-derivations on appropriate subsets in prime rings.
doi_str_mv 10.3842/umzh.v76i2.654
first_indexed 2026-03-24T02:03:36Z
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fulltext Skip to main content Log in Menu Find a journal Publish with us Track your research Search Saved research Cart Home Ukrainian Mathematical Journal Article On Multiplicative (Generalized)-(α, β)-Derivations in Prime Rings Published: 16 August 2024 Volume 76, pages 318–329, (2024) Cite this article Save article View saved research Ukrainian Mathematical Journal Aims and scope Submit manuscript Chirag Garg1 & R. K. Sharma2  47 Accesses Explore all metrics We discuss some algebraic identities related to multiplicative (generalized) derivations and multiplicative (generalized)-(α, β)-derivations on appropriate subsets in prime rings. This is a preview of subscription content, log in via an institution to check access. Access this article Log in via an institution Subscribe and save Springer+ from €37.37 /Month Starting from 10 chapters or articles per month Access and download chapters and articles from more than 300k books and 2,500 journals Cancel anytime View plans Buy Now Buy article PDF 39,95 € Price includes VAT (Ukraine) Instant access to the full article PDF. Institutional subscriptions Similar content being viewed by others On Commutativity with Generalized Derivations Acting on Prime Rings and Banach Algebras Chapter © 2025 On generalized derivations involving prime ideals Article 13 July 2021 Some Algebraic Identities in 3-Prime Near-Rings Article 01 June 2020 Explore related subjects Discover the latest articles, books and news in related subjects, suggested using machine learning. Algebraic Geometry Algebra Associative Rings and Algebras Category Theory, Homological Algebra Commutative Rings and Algebras Non-associative Rings and Algebras Generalized Derivations in Algebraic Structures References E. Albas, “Generalized derivations on ideals of prime rings,” Miskolc Math. Notes, 14, 3–9 (2002). Article  MathSciNet  Google Scholar  S. Ali, B. Dhara, N. A. Dar, and A. N. Khan, “On Lie ideals with multiplicative (generalized)-derivations in prime and semiprime rings,” Beitr. Algebra Geom. (2014); https://doi.org/10.1007/s13366-013-186-y. Article  Google Scholar  M. Ashraf and N. Rehman, “On commutativity of rings with derivations,” Res. Math., 42, 3–8 (2002). Article  MathSciNet  Google Scholar  H. E. Bell and M. N. Daif, “On derivations and commutativity in prime rings,” Acta Math. Hungar., 66, 337–343 (1995). Article  MathSciNet  Google Scholar  J. Bergen, I. N. Herstein, and J. W. Kerr, “Lie ideals and derivations of prime rings,” J. Algebra, 71, 259–267 (1981). Article  MathSciNet  Google Scholar  M. Brešar, “On the distance of the composition of two derivations to the generalized derivations,” Glasgow Math. J., 33, 89–93 (1991). Article  MathSciNet  Google Scholar  M. N. Daif and H. E. Bell, “Remarks on derivations on semiprime rings,” Int. J. Math. Math. Sci., 15, 205–206 (1992). Article  MathSciNet  Google Scholar  M. N. Daif and M. S. Tammam El-Sayiad, “Multiplicative generalized derivations which are additive,” East-West J. Math., 9, 31–37 (1997). M. N. Daif, “When is a multiplicative derivation additive,” Int. J. Math. Math. Sci., 14, 615–618 (1991). Article  MathSciNet  Google Scholar  B. Dhara and S. Ali, “On multiplicative (generalized)-derivations in prime and semiprime rings,” Aequation. Math., 86, 65–79 (2013). Article  MathSciNet  Google Scholar  B. Dhara, S. Kar, and D. Das, “A multiplicative (generalized)-(σ, σ)-derivation acting as (anti-)homomorphism in semiprime rings,” Palest. J. Math., 3, 240–246 (2014). MathSciNet  Google Scholar  C. Garg and R. K. Sharma, “On generalized (α, β)-derivations in prime rings,” Rend. Circ. Mat. Palermo (2), 65, 175–184 (2016). Article  Google Scholar  O. Golbasi and E. Koc, “Generalized derivations of Lie ideals in prime rings,” Turkish J. Math., 35, 23–28 (2011). MathSciNet  Google Scholar  H. Goldmann and P. Šemrl, “Multiplicative derivations on C(X),” Monatsh. Math., 121, 189–197 (1996). Article  MathSciNet  Google Scholar  S. Khan, “On semiprime rings with multiplicative (generalized)-derivations,” Beitr. Algebra Geom. (2015); https://doi.org/10.1007/s13366-015-0241-y. Article  Google Scholar  E. C. Posner, “Derivations in prime rings,” Proc. Amer. Math. Soc., 8, 1093–1100 (1957). Article  MathSciNet  Google Scholar  N. Rehman, “On commutativity of rings with generalized derivations,” Math. J. Okayama Univ., 44, 43–49 (2002). MathSciNet  Google Scholar  Download references Author information Authors and Affiliations Department of Mathematics, Deshbandhu College, University of Delhi, Delhi, India Chirag Garg Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India R. K. Sharma Authors Chirag GargView author publications Search author on:PubMed Google Scholar R. K. SharmaView author publications Search author on:PubMed Google Scholar Corresponding author Correspondence to Chirag Garg. Additional information Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, No. 2, pp. 289–297, February, 2024. Ukrainian DOI: https://doi.org/10.3842/umzh.v76i2.654. 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spelling umjimathkievua-article-6542024-06-19T00:35:09Z On multiplicative (generalized)-$(\alpha,\beta)$-derivations in prime rings On multiplicative (generalized)-$(\alpha,\beta)$-derivations in prime rings Garg, Chirag Sharma, R. K. Garg, Chirag Sharma, R. K. multiplicative (generalized)-derivations UDC 512.5 We discuss some algebraic identities related to multiplicative (generalized)-derivations and multiplicative (generalized)-$(\alpha,\beta)$-derivations on appropriate subsets in prime rings. УДК 512.5 Про мультиплікативні (узагальнені) $(\alpha,\beta)$-похідні в простих кільцях Вивчаються деякі алгебраїчні  тотожності, що пов'язані з мультиплікативними (узагальненими) похідними та мультиплікативними (узагальненими) $(\alpha,\beta)$-похідними на відповідних підмножинах у простих кільцях. Institute of Mathematics, NAS of Ukraine 2024-02-28 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/654 10.3842/umzh.v76i2.654 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 2 (2024); 289-297 Український математичний журнал; Том 76 № 2 (2024); 289-297 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/654/9730
spellingShingle Garg, Chirag
Sharma, R. K.
Garg, Chirag
Sharma, R. K.
On multiplicative (generalized)-$(\alpha,\beta)$-derivations in prime rings
title On multiplicative (generalized)-$(\alpha,\beta)$-derivations in prime rings
title_alt On multiplicative (generalized)-$(\alpha,\beta)$-derivations in prime rings
title_full On multiplicative (generalized)-$(\alpha,\beta)$-derivations in prime rings
title_fullStr On multiplicative (generalized)-$(\alpha,\beta)$-derivations in prime rings
title_full_unstemmed On multiplicative (generalized)-$(\alpha,\beta)$-derivations in prime rings
title_short On multiplicative (generalized)-$(\alpha,\beta)$-derivations in prime rings
title_sort on multiplicative (generalized)-$(\alpha,\beta)$-derivations in prime rings
topic_facet multiplicative (generalized)-derivations
url https://umj.imath.kiev.ua/index.php/umj/article/view/654
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