Generalized Semiderivations and Semimultipliers in Semiprime Ideals
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Abstract
In this study, we examine the behavior of a ring A when it admits a generalized semiderivation Φ associated with a semiderivation Ω and a mapping σ, as well as semimultipliers T within its semiprime ideals P. More specifically, the present work investigates differential identities in the semiprime ideal of an arbitrary ring using P-commuting semiderivations.
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[1] K. Didem Camci and Neset Aydin. On multiplicative (generalized)-derivations in semiprime rings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1):153–164, 2017.
[2] G. Naga Malleswari, S. Sreenivasulu, and G. Shobhalatha. Semiprime rings with multiplicative (generalized)-derivations involving left multipliers. Creative Mathematics and Informatics, 30(1):61–68, 2021.
[3] Joso Vukman. Centralizers on semiprime rings. Commentationes Mathematicae Universitatis Carolinae, 42(2):237–245, 2001.
[4] Joso Vukman. An identity related to centralizers in semiprime rings. Commentationes Mathematicae Universitatis Carolinae, 40:447–456, 1999.
[5] Borut Zalar. On centralizers of semiprime rings. Commentationes Mathematicae Universitatis Carolinae, 32(4):609–614, 1991.
[6] Jeffrey Bergen. Derivations in prime rings. Canadian Mathematical Bulletin, 26(3):267–270, 1983.
[7] Kyung Ho Kim. A note on semimultipliers in prime rings. Electronic Journal of Mathematical Analysis and Applications, 6(1):204–212, 2018.
[8] Basudeb Dhara. Generalized derivations acting as a homomorphism or anti-homomorphism in semiprime rings. Beitrage zur Algebra und Geometrie, 53(1):203–209, 2012.
[9] Emine Albas. Generalized derivations on ideals of prime rings. Miskolc Mathematical Notes, 14(1):3–9, 2013.
[10] Asma Ali, Deepak Kumar, and Phool Miyan. On generalized derivations and commutativity of prime and semiprime rings. Hacettepe Journal of Mathematics and Statistics, 40(3):367–374, 2011.
[11] Mehsin Jabel Atteya. On generalized derivations of semiprime rings. International Journal of Algebra, 4(12):591–598, 2010.
[12] G. Naga Malleswari, S. Sreenivasulu, and G. Shobhalatha. Some identities involving multiplicative (generalized) (alpha,1)-derivations in semiprime rings. Journal of the Indonesian Mathematical Society, 28(1):44–51, 2022.
[13] Hafedh M. Alnoghashi, Sabah Naji, Nadeem ur Rehman, and Li Guo. On multiplicative (generalized)-derivation involving semiprime ideals. Journal of Mathematics, 2023:1–7, 2023.
[14] Shuliang Huang. Generalized derivations of sigma-prime rings. International Journal of Algebra, 2(18):867–873, 2008.
[15] Kyung Ho Kim. A note on star-semimultipliers in prime rings with involution. Electronic Journal of Mathematical Analysis and Applications, 8(1):192–198, 2020.
[16] Ajda Fosner and Mehsin Jabel Atteya. Semigeneralized semiderivations of semiprime rings. In AIP Conference Proceedings, volume 2037, page 020010, 2018.
[17] G. Naga Malleswari and S. Sreenivasulu. On skew jordan product and generalized derivations in prime rings with involution. JP Journal of Algebra, Number Theory and Applications, 63(4):329–334, 2024.
[18] G. Naga Malleswari, S. Sreenivasulu, and G. Shobhalatha. Centralizing properties of (alpha,1)-derivations in semiprime rings. International Journal of Mathematics and its Applications, 8(1):127–132, 2020.
[19] Oznur Golbasi and Onur Agirtici. Multiplicative semiderivations on ideals of semiprime rings. Palestine Journal of Mathematics, 9(2):792–800, 2020.
[20] Oznur Golbasi and Zeliha Bedir. Some identities involving multiplicative semiderivations on ideals. Hacettepe Journal of Mathematics and Statistics, 50(4):963–969, 2021.