Some Results on Double Cenralizer for Prime and Semiprime Г- rings

Aya Hussein; Abdulahman H.  Majeed; Shrooq Bahjat  Smeein; Azza I.M.S.  Abu-Shams

doi:10.30526/38.2.3594

Authors

Aya Hussein Department of Mathematics, College, of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0009-0002-8259-4959
Abdulahman H. Majeed Department of Mathematic, Al-Mamoun University College, Baghdad, Iraq https://orcid.org/0000-0001-8534-0749
Shrooq Bahjat Smeein Department of Mathematics, An-Najah National University, Nablus P400, Palestine. https://orcid.org/0009-0002-9351-4176
Azza I.M.S. Abu-Shams Information Department -Section Mathematics, University of Technology and Applied Science - Muscat, Sultanate of Oman. https://orcid.org/0009-0003-1741-1447

DOI:

https://doi.org/10.30526/38.2.3594

Keywords:

Keywords: Prime Г- rings , Semiprime Г- rings, centralizer, Jordan centralizer, double centralizer, double Jordan centralizer.

Abstract

The goal of this work, is to examine the concept of a double centralizer, and double Jordan centralizer on prime and semiprime Г-rings, this is done by studying examples, remarks and results related to that concepts and looking for the conditions under which T equal S, we prove the results, the first result, let A be a semiprime Γ-ring and T is a left centralizer, S is a right centralizer, and they fulfilling x T(y) = S (x) y, for each x A, Γ, thence (T,S) is a double centralizer. The second, let A be a prime Γ-ring, U be a not equal zero ideal of A, such that, T is a left centralizer, S is a right centralizer, and fulfilling x T(y) = S (x) y, for each x, y U, Γ, thence (T, S) is a double centralizer. The third, let A be a prime Γ-ring, U be a non-zero ideal of A, and we get , if T=S on U, thence T=S on A.

Author Biographies

Aya Hussein, Department of Mathematics, College, of Science, University of Baghdad, Baghdad, Iraq

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Abdulahman H. Majeed , Department of Mathematic, Al-Mamoun University College, Baghdad, Iraq

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Shrooq Bahjat Smeein , Department of Mathematics, An-Najah National University, Nablus P400, Palestine.

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Azza I.M.S. Abu-Shams , Information Department -Section Mathematics, University of Technology and Applied Science - Muscat, Sultanate of Oman.

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