Research Article

Some Characterizations of $h$-Regular $\Gamma$-Hemiring in terms of Cubic $h$-Ideals

Volume: 3 Number: 4 December 22, 2020
EN

Some Characterizations of $h$-Regular $\Gamma$-Hemiring in terms of Cubic $h$-Ideals

Abstract

The aim of this paper is to study $h$-hemiregular and $h$-intra-hemiregular $\Gamma$-hemiring using the combined concept of cubic set and \textit{h}-ideals.We have defined two types of compositions of cubic sets and used these to obtain some characterizations of $h$-hemiregular and $h$-intra-hemiregular $\Gamma$-hemiring.

Keywords

Γ-hemiring, cubic h-ideal, h-intra-hemiregular, h-hemiregular

References

  1. [1] V. Chinnadurai, K. Bharathivelan, Cubic bi-ideals in near-rings, International Journal of computer and Mathematical Sciences, Vol. 5, Issue 2(2016) 44 - 52
  2. [2] V. Chinnadurai, K. Bharathivelan, Cubic Lateral Ideals in Ternary Near - Rings, International Advanced Research Journal in Science, Engineering and Technology, Vol. 3, Issue11(November 2016) 209 - 215
  3. [3] J.S.Golan, Semirings and their applications, Kluwer Academic Publishers,1999.
  4. [4] M. Henriksen, Ideals in semirings with commutative addition, Amer. Math. Soc. Notices, 6(1958) 321.
  5. [5] K.Iizuka, On the Jacobson radical of semiring, Tohoku Math.J., Vol.11 No. 2(1959), 409-421
  6. [6] Y.B. Jun, M.A.Ozt¨ urk, S.Z.Song,¨ On Fuzzy h-ideals in hemiring, Information sciences, 162(2004), 211-226.
  7. [7] Y.B. Jun, S.T. Jung and M.S. Kim, Cubic subgroups, Annals of Fuzzy Mathematics and Informatics, 2(2011), 9 - 15.
  8. [8] Y.B. Jun, C.S. Kim and K.O. Yang, Cubic sets, Annals of Fuzzy Mathematics and Informatics, 4(2012), 83 - 98.
  9. [9] A. Khan, Y.B. Jun, S.I.A. Shah, M. Ali, Characterizations of hemirings in terms of cubic h-ideals, Soft Comput, DOI 10.1007/s00500-014-1396-4
  10. [10] D.R.La Torre, On h-ideals and k-ideals in hemirings,Publ. Math. Debrecen 12(1965), 219-226.
APA
Mandal, D. (2020). Some Characterizations of $h$-Regular $\Gamma$-Hemiring in terms of Cubic $h$-Ideals. Communications in Advanced Mathematical Sciences, 3(4), 218-224. https://doi.org/10.33434/cams.746503
AMA
1.Mandal D. Some Characterizations of $h$-Regular $\Gamma$-Hemiring in terms of Cubic $h$-Ideals. Communications in Advanced Mathematical Sciences. 2020;3(4):218-224. doi:10.33434/cams.746503
Chicago
Mandal, Debabrata. 2020. “Some Characterizations of $h$-Regular $\Gamma$-Hemiring in Terms of Cubic $h$-Ideals”. Communications in Advanced Mathematical Sciences 3 (4): 218-24. https://doi.org/10.33434/cams.746503.
EndNote
Mandal D (December 1, 2020) Some Characterizations of $h$-Regular $\Gamma$-Hemiring in terms of Cubic $h$-Ideals. Communications in Advanced Mathematical Sciences 3 4 218–224.
IEEE
[1]D. Mandal, “Some Characterizations of $h$-Regular $\Gamma$-Hemiring in terms of Cubic $h$-Ideals”, Communications in Advanced Mathematical Sciences, vol. 3, no. 4, pp. 218–224, Dec. 2020, doi: 10.33434/cams.746503.
ISNAD
Mandal, Debabrata. “Some Characterizations of $h$-Regular $\Gamma$-Hemiring in Terms of Cubic $h$-Ideals”. Communications in Advanced Mathematical Sciences 3/4 (December 1, 2020): 218-224. https://doi.org/10.33434/cams.746503.
JAMA
1.Mandal D. Some Characterizations of $h$-Regular $\Gamma$-Hemiring in terms of Cubic $h$-Ideals. Communications in Advanced Mathematical Sciences. 2020;3:218–224.
MLA
Mandal, Debabrata. “Some Characterizations of $h$-Regular $\Gamma$-Hemiring in Terms of Cubic $h$-Ideals”. Communications in Advanced Mathematical Sciences, vol. 3, no. 4, Dec. 2020, pp. 218-24, doi:10.33434/cams.746503.
Vancouver
1.Debabrata Mandal. Some Characterizations of $h$-Regular $\Gamma$-Hemiring in terms of Cubic $h$-Ideals. Communications in Advanced Mathematical Sciences. 2020 Dec. 1;3(4):218-24. doi:10.33434/cams.746503