ON JORDAN IDEAL IN PRIME AND SEMIPRIME INVERSE SEMIRINGS WITH CENTRALIZER

Authors

  • Rawnaq Khaleel Ibraheem Math Department, College of Science, University of Baghdad.
  • Abdulrahman H. Majeed Math Department, College of Science, University of Baghdad. http://orcid.org/0000-0001-8534-0749

DOI:

https://doi.org/10.23851/mjs.v30i4.710

Keywords:

Additively inverse semiring, Jordan ideal of an inverse semiring, Semiprime inverse semirings .

Abstract

     In this paper we recall the definition of centralizer on inverse semiring. Also introduce the definition of Jordan ideal and Lie ideal. Some results of M.A.Joso Vukman on centralizers on semiprime rings are generalized here to inverse semirings.

Author Biography

Abdulrahman H. Majeed, Math Department, College of Science, University of Baghdad.

mathematics

References

Golan, J. S., The Theory of Semirings With Applications in Mathematics and Theoretical Computer Science, Longman Scientific and Technical, UK, 1992.

Joso Vukman, Centralizers on semiprime rings, Comment. Math Univ. Carolinae 42,V.2, 237-245. 2001.

Joso Vukman, An identity related to centralizers in semiprime rings, Comment. Math Univ. Carolinae 406, V.3, 447-456. 1999.

Joso Vukman, Centralizers on prime and semiprime rings, Comment. Math. Univ. Carolinae 38,V.2, 231-240. 1997. [CrossRef]

Karvellas, P.H. Inversive semirings, J.Austral Math Soc. 18: 277-288. 1974. [CrossRef]

Ram Awtar, Jordan structure in semiprime rings, Can.j.math, 3, VxxvIII, No.5,1067-1072. 1976. [CrossRef]

Rawnaq, KH. And Abdulrahman H. Majeed, On Lie Structure in Semiprime Inverse Semirings, IRAQ JOURNAL OF SCIENCE, to appear in issue (12), Volume (60) 2019.

Shafiq S. and Aslam, M. and JAVED, M.A. Centralizer of Inverse Semiring, General Algebra and Applications 3671-84(2016).

Shafiq, S. and Aslam, M., On Jordan mapping of inverse semirings, De Gruyter, Open Math. 15: 1123-1131, 2017. [CrossRef]

Shaker. H.A, Centralizers on prime and semiprimerings, Baghdad University (Iraq). Msc. Thesis, 2005.

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Published

2020-01-15

How to Cite

[1]
R. K. Ibraheem and A. H. Majeed, “ON JORDAN IDEAL IN PRIME AND SEMIPRIME INVERSE SEMIRINGS WITH CENTRALIZER”, MJS, vol. 30, no. 4, pp. 77–87, Jan. 2020.

Issue

Section

Mathematics