Research article

On centrally extended mappings that are centrally extended additive

  • Received: 12 August 2024 Revised: 30 October 2024 Accepted: 14 November 2024 Published: 21 November 2024
  • MSC : 16N60, 16U80, 16W25

  • This paper aims to establish the following: Let $ \Omega $ be a ring that satisfies some conditions and has an idempotent element $ f\neq 0, 1 $. We intend to show that if $ G $ is any suitable multiplicative generalized CE-derivation of $ \Omega $, then $ G $ is a centrally extended additive.

    Citation: M. S. Tammam El-Sayiad, Munerah Almulhem. On centrally extended mappings that are centrally extended additive[J]. AIMS Mathematics, 2024, 9(11): 33254-33262. doi: 10.3934/math.20241586

    Related Papers:

  • This paper aims to establish the following: Let $ \Omega $ be a ring that satisfies some conditions and has an idempotent element $ f\neq 0, 1 $. We intend to show that if $ G $ is any suitable multiplicative generalized CE-derivation of $ \Omega $, then $ G $ is a centrally extended additive.



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    [2] S. F. El-Deken, M. M. El-Soufi, On centrally extended reverse and generalized reverse derivations, Indian J. Pure Appl. Math., 51 (2020), 1165–1180. https://doi.org/10.1007/s13226-020-0456-y doi: 10.1007/s13226-020-0456-y
    [3] S. F. El-Deken, H. Nabiel, Centrally-extended generalized $\ast$-derivations on rings with involution, Beitr. Algebra Geom., 60 (2019), 217–224. https://doi.org/10.1007/s13366-018-0415-5 doi: 10.1007/s13366-018-0415-5
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    [6] C. E. Rickart, One-to-one mappings of rings and lattices, Bull. Amer. Math. Soc., 54 (1948), 758–764.
    [7] W. S. Martindale, When are multiplicative mappings additive?, Proc. Amer. Math. Soc., 21 (1969), 695–698. https://doi.org/10.1090/S0002-9939-1969-0240129-7 doi: 10.1090/S0002-9939-1969-0240129-7
    [8] M. N. Daif, When is a multiplicative derivation additive?, Int. J. Math. Math. Sci., 14 (1991), 275743. https://doi.org/10.1155/S0161171291000844 doi: 10.1155/S0161171291000844
    [9] Y. Wang, The additivity of multiplicative maps on rings, Commun. Algebra, 37 (2009), 2351–2356. https://doi.org/10.1080/00927870802623369 doi: 10.1080/00927870802623369
    [10] J. C. M. Ferreira, B. L. M. Ferreira, Additivity of n-multiplicative maps on alternating rings, Commun. Algebra, 44 (2016), 1557–1568. https://doi.org/10.1080/00927872.2015.1027364 doi: 10.1080/00927872.2015.1027364
    [11] B. L. M. Ferreira, H. Guzzo, R. N. Ferreira, An approach between the multiplicative and additive structure of a Jordan ring, Bull. Iran. Math. Soc., 47 (2021), 961–975. https://doi.org/10.1007/s41980-020-00423-4 doi: 10.1007/s41980-020-00423-4
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