Jordan Higher ⋆-Left (Accordingly Right)-Centralizers on Prime Rings With Involution

Authors

  • Auday Hekmat Mahmood Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq.
  • Salah Mehdi Salih Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq.
  • Radwan Mohammed Al-Omary Department of Mathematics, Ibb University, Ibb, Yemen.

Keywords:

Higher centralizer , Prime Ring with involution

Abstract

In this paper we introduce the concepts higher ⋆-left (accordingly right) centralizer, Jordan higher ⋆-left (accordingly right) centralizer. We prove Any J H⋆L(AR) C on prime ring R has characteristic different from 2 with involution is  H⋆L(AR) C on R.

References

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[2] Alahamdi, A.; Alhazmi, H.; Ali, A.; Khan, A.N.; "A characterization of Jordan left ∗-centralizers in rings with involution". Appl. Math. Information Sci., 11(2): 441-447, 2017.

[3] Bhushana, B.; Sandhub, G.S.; Alic, S.; Kumar, D.; "A classification of generalized derivations in rings with involution". Filomat, 35(5): 1439 -1452, 2021.

[4] Ferro, M.; Heatinger, C.; "Higher derivations and a theorem by Herstien". Quaestions Math., 25: 1-9, 2002.

[5] Herstein, I.N.; "Topics in Rings Theory".2ed edition; The University of Chicago Press, USA, 1969.

[6] Thahab, H.J.; Salih, S.M.; "On Jordan generalized symmetric higher bi-left (resp.right) centralizers on prime

[7] Salih, S.M.; Abd Ali, H.H.; "Orthogonal generalized higher k-derivations on semi prime Г-rings". Iraqi J. Sci., 64(2): 834-841, 2023.

[8] Sulaiman, N.N.; Salih, S.M.; "Generalized Jordan triple (σ,τ)-higher homomorphisms on prime rings". Al-Nahrain J. Sci., 23(3): 76-82, 2020.

[9] Ibraheem, R.K.; Majeed, A.H.; "On Jordan ideal in prime and semiprime inverse semirings with centralizer". Al-Mustansiriyah J. Sci., 30(4): 77-87, 2019.

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Published

2025-06-15

Issue

Vol. 28 No. 2 (2025): June 2025

Section

Mathematics

License

Copyright (c) 2025 Auday Hekmat Mahmood, Salah Mehdi Salih, Radwan Mohammed Al-Omary

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

(1)
Hekmat Mahmood, A. .; Mehdi Salih, S. .; Mohammed Al-Omary, R. . Jordan Higher ⋆-Left (Accordingly Right)-Centralizers on Prime Rings With Involution. Al-Nahrain J. Sci. 2025, 28 (2), 189-191.