Construction of k-Hyperideals by P-Hyperoperations

Authors

  • H. Hedayati Department of Mathematics, Faculty of Basic Science, University of Mazandaran, Babolsar, Iran
  • R. Ameri Department of Mathematics, Faculty of Basic Science, University of Mazandaran, Babolsar, Iran

Keywords:

(semi)hyperring, k-(hyper)ideal, P-hyperoperation, weak distributive

Abstract

In this note we present a method to construction new k-hyperideals from given k-ideals of a semiring R by using of the P-hyperoperations. Then we investigate the relationship between them. In particular, we describe all khyperideals of the semihyperring of the nonnegative integers.

References

R. Ameri, and M. M. Zahedi, ”Hyperalgebraic System”, Italian Journal of Pure and Applied Mathematics, No. 6 (1999) 21-32.

P. Corsini, ”Prolegomena of Hypergroup Theory”, second edition Aviani editor, (1993).

P. Corsini, and V. Leoreanu, ”Applications of Hyperstructure Theory”, Kluwer Academic Publications (2003).

D. Freni, ” A New Characterization of the Derived Hypergroup via Strongly Regular Equivalences ”, Communication In Algebra, Vol. 30, No. 8 (2002), pp. 3977-3989

H. Hedayati, and R. Ameri,” Fuzzy k-hyperideals ”, Int. J. Pu. Appl. Math.Sci., Vol. 2, No. 2, (to appear).

H. Hedayati, and R. Ameri, ” On k-Hyperideals of Semihyperrings”, (to appear).

S. Ioudilis, Polygroups et certaines de leurs proprietes, Bull. Greek. Math. Soc., vol. 22 (1981) 95-103.

J. Jantosciak, ”Transposition Hypergroups: Noncommutative Join Spaces”, J. of Algebra , Vol. 187 (1997) 97-119.

J. Jantosciak, Homomorphism, Equivalences and Reductions in Hypergroups, Rivista di Matematica Pure ed Applicata, No. 9(1991) 23-47.

M. Krasner, ”Approximation des Corps Values Complets de Caracteristque P 6= 0 Par Ceux de aracteristique 0”, Actes due Colloque d, Algebre Superieure C.B.R.M, Bruxelles, (1965) 12-22.

D.R. Latore, ”On h-ideals and k-ideals in hemirings”, Pub. Math. Debrecen, 12 (1965) 219-226

F. Marty, ”Surnue generaliz-ation de la notion de group”, 8iem cou Scandinaves Stockholm, (1934) 45-49.

I. G. Rosenberg, Hypergroups and Join Spaces determined by relations, Italian J. of Pure and Applied Math., N. 4, (1998), 93-101.

M. K. Sen, and M. R. Adhikari, ” On Maximal k-ideals in Semirings”, Proceedings of the American Mathematics Society, Vol. 118, No. 3, July 1993.

T. Vougiuklis, ”Hyperstructures and their representations”, Hardonic Press, Inc. (1994).

H. J. Weinert, and M. K. Sen, and M. R. Adhikari, ” One-sided k-ideals and h-ideals in Semirings”, Mathematica Pannonica, 7/1 (1996), 147-162.

Downloads

Published

2005-06-18

Issue

Vol. 15 (2005)

Section

Volume 15-2005

License

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:

  • Free access for all users worldwide
  • Increased visibility and readership
  • Rapid publication
  • No spatial constraints
  • Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)

Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. 
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.