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Study of multiplicative $b$-generalized derivation and its additivity | ||
| Journal of Algebra and Related Topics | ||
| دوره 11، شماره 1، شهریور 2023، صفحه 111-121 اصل مقاله (262.58 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2023.23051.1444 | ||
| نویسندگان | ||
| M. R. Mozumder* ؛ W. Ahmed | ||
| Department of Mathematics, Aligarh Muslim University, Aligarh, India | ||
| چکیده | ||
| Our intention in this paper is to prove the following. Let R be a ring with an idempotent element (0, 1 ̸=)e and f be a multiplicative b-generalized derivation on R. Then we show that f is additive by imposing certain conditions on the ring R. | ||
| کلیدواژه‌ها | ||
| Associative ring؛ derivation؛ multiplicative b-generalized derivation؛ pierce decomposition | ||
| مراجع | ||
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1. M. N. Daif, When is a multiplicative derivation additive?, Int. J. Math. and Math. Sci., (3) 14 (1991), 615-618. 2. M. N. Daif and M. S. Tammam-El-Sayiad, Multiplicative generalized derivations which are additive, East-West J. Math., (1) 9 (1997), 31-37. 3. N. Jacobson, Structure of rings, Amer. Math. Soc. Colloq. Publ., 37 (1964). 4. W. S. Martindale, When are multiplicative mappings additive?, Proc. Amer. Math. Soc., (3) 21 (1969), 695-698. 5. N. Rehman, M. Hafedh Alnoghashi and M. Hongan, A note on generalized derivations on prime ideals, J. Algebra Relat. Topics, (1) 10 (2022), 159-169. 6. E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100. 7. Y. Wang, The additivity of multiplicative maps on rings, Comm. Alg., (6) 37 (2009), 2351-2356. | ||
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