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Some Commutativity Criteria for Prime Rings with Involution Involving Symmetric and Skew Symmetric Elements

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Ukrainian Mathematical Journal Aims and scope

We study the Posner second theorem [Proc. Amer. Math. Soc., 8, 1093–1100 (1957)] and strong commutativity preserving problem for symmetric and skew symmetric elements involving generalized derivations on prime rings with involution. The obtained results cover numerous known theorems. We also provide examples showing that the obtained results hold neither in the case of involution of the first kind, nor in the case where the ring is not prime.

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Authors and Affiliations

  1. Government Higher Secondary School, Kaprin, Shopian Jammu and Kashmir, India

    N. A. Dar

  2. Aligarh Muslim University, Aligarh, India

    S. Ali

  3. Madanpalle Institute of Technology and Science, Madanpalle, India

    A. Abbasi

  4. Aligarh Muslim University, Aligarh, India

    M. Ayedh

Authors
  1. N. A. Dar
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  2. S. Ali
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  3. A. Abbasi
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  4. M. Ayedh
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Corresponding author

Correspondence to S. Ali.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 4, pp. 455–466, April, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i4.6751.

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Dar, N.A., Ali, S., Abbasi, A. et al. Some Commutativity Criteria for Prime Rings with Involution Involving Symmetric and Skew Symmetric Elements. Ukr Math J 75, 519–534 (2023). https://doi.org/10.1007/s11253-023-02214-6

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  • DOI: https://doi.org/10.1007/s11253-023-02214-6

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