A REMARK ON CENTRALIZERS IN SEMIPRIME INVERSE SEMIRINGS

Authors:

D. Mary Florence,R. Murugesan,P. Namasivayam,

DOI NO:

https://doi.org/10.26782/jmcms.2020.06.00026

Keywords:

Semiprime Semiring,Inverse Semiring,Commutator,Centralizer,Left (right) Centralizer,

Abstract

Let be an additive mapping of a 2-torsion free semiprime inverse semiring in to itself, satisfying holds for all , then is a centralizer.

Refference:

I. Bandlet and Petrich, Subdirect products of rings and distributive lattices, Proceedings of the Edinburgh Mathematical Society, 25, 155-171 (1982).
II. Golan, The theory of semirings with applications in mathematics and theoretical computer science, Longman Scientific & Technical; New York: Wiley, (1992).
III. Javed, Aslam and Hussain, On Condition (A2) of Bandlet and Petrich for inverse semirings, International Mathematical Forum, Vol.7, 2903−2914 (2012).
IV. Karvellas P.H., Inversivesemirings, J. Aust. Math. Soc. 18, 277 – 288 (1974).
V. Maryam K. Rasheed, Abdulrahman. H. Majeed, Some results of (α, β) derivations on prime semirings, Iraqi Journal of Science, Vol. 60, No.5, pp: 1154-116 (2019).
VI. Sara, Aslam and Javed, Oncentralizer of semiprime inverse semiring, Discuss. Math. Gen. Algebra and Applications, 36, 71 – 84 (2016).
VII. M. K. Sen and S. K. Maity, Regular additively inverse semirings, Acta Math. Univ. Comenianae, 1, 137-146 (2006).
VIII. Vukman, An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolin. 40, 3, 447–456 (1999).

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