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Year 2020, Volume: 3 Issue: 4, 218 - 224, 22.12.2020
https://doi.org/10.33434/cams.746503

Abstract

References

  • [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] 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] J.S.Golan, Semirings and their applications, Kluwer Academic Publishers,1999.
  • [4] M. Henriksen, Ideals in semirings with commutative addition, Amer. Math. Soc. Notices, 6(1958) 321.
  • [5] K.Iizuka, On the Jacobson radical of semiring, Tohoku Math.J., Vol.11 No. 2(1959), 409-421
  • [6] Y.B. Jun, M.A.Ozt¨ urk, S.Z.Song,¨ On Fuzzy h-ideals in hemiring, Information sciences, 162(2004), 211-226.
  • [7] Y.B. Jun, S.T. Jung and M.S. Kim, Cubic subgroups, Annals of Fuzzy Mathematics and Informatics, 2(2011), 9 - 15.
  • [8] Y.B. Jun, C.S. Kim and K.O. Yang, Cubic sets, Annals of Fuzzy Mathematics and Informatics, 4(2012), 83 - 98.
  • [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] D.R.La Torre, On h-ideals and k-ideals in hemirings,Publ. Math. Debrecen 12(1965), 219-226.
  • [11] X.Ma, J.Zahn, Fuzzy h-ideals in h-hemiregular and h-semisimple Γ-hemirings, Neural Comput and Applic, 19(2010), 477-485
  • [12] D. Mandal, On Cubic h-ideals ofΓ-hemiring, Bull. Int. Math. Virtual Inst., Vol. 10, No.3, (2020), 567-579.
  • [13] S. K. Sardar, D. Mandal, On fuzzy h-ideals in h-regular Γ-hemiring and h-duo Γ-hemiring, Gen. Math. Notes, Vol. 2 No. 1,(2011), 64-85
  • [14] S.K.Sardar, D.Mandal, On fuzzy h-ideal in Γ-hemiring, Int. J. Pure. Appl. Math, Vol. 56, No. 3(2009),439-450
  • [15] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35(1971), 512-517
  • [16] L.A.Zadeh, Fuzzy Sets, Information and Control, 8(1965), 338-353.

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

Year 2020, Volume: 3 Issue: 4, 218 - 224, 22.12.2020
https://doi.org/10.33434/cams.746503

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.

References

  • [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] 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] J.S.Golan, Semirings and their applications, Kluwer Academic Publishers,1999.
  • [4] M. Henriksen, Ideals in semirings with commutative addition, Amer. Math. Soc. Notices, 6(1958) 321.
  • [5] K.Iizuka, On the Jacobson radical of semiring, Tohoku Math.J., Vol.11 No. 2(1959), 409-421
  • [6] Y.B. Jun, M.A.Ozt¨ urk, S.Z.Song,¨ On Fuzzy h-ideals in hemiring, Information sciences, 162(2004), 211-226.
  • [7] Y.B. Jun, S.T. Jung and M.S. Kim, Cubic subgroups, Annals of Fuzzy Mathematics and Informatics, 2(2011), 9 - 15.
  • [8] Y.B. Jun, C.S. Kim and K.O. Yang, Cubic sets, Annals of Fuzzy Mathematics and Informatics, 4(2012), 83 - 98.
  • [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] D.R.La Torre, On h-ideals and k-ideals in hemirings,Publ. Math. Debrecen 12(1965), 219-226.
  • [11] X.Ma, J.Zahn, Fuzzy h-ideals in h-hemiregular and h-semisimple Γ-hemirings, Neural Comput and Applic, 19(2010), 477-485
  • [12] D. Mandal, On Cubic h-ideals ofΓ-hemiring, Bull. Int. Math. Virtual Inst., Vol. 10, No.3, (2020), 567-579.
  • [13] S. K. Sardar, D. Mandal, On fuzzy h-ideals in h-regular Γ-hemiring and h-duo Γ-hemiring, Gen. Math. Notes, Vol. 2 No. 1,(2011), 64-85
  • [14] S.K.Sardar, D.Mandal, On fuzzy h-ideal in Γ-hemiring, Int. J. Pure. Appl. Math, Vol. 56, No. 3(2009),439-450
  • [15] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35(1971), 512-517
  • [16] L.A.Zadeh, Fuzzy Sets, Information and Control, 8(1965), 338-353.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Debabrata Mandal

Publication Date December 22, 2020
Submission Date June 1, 2020
Acceptance Date December 17, 2020
Published in Issue Year 2020 Volume: 3 Issue: 4

Cite

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 Mandal D. Some Characterizations of $h$-Regular $\Gamma$-Hemiring in terms of Cubic $h$-Ideals. Communications in Advanced Mathematical Sciences. December 2020;3(4):218-224. doi:10.33434/cams.746503
Chicago Mandal, Debabrata. “Some Characterizations of $h$-Regular $\Gamma$-Hemiring in Terms of Cubic $h$-Ideals”. Communications in Advanced Mathematical Sciences 3, no. 4 (December 2020): 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 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, 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 2020), 218-224. https://doi.org/10.33434/cams.746503.
JAMA 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, 2020, pp. 218-24, doi:10.33434/cams.746503.
Vancouver Mandal D. Some Characterizations of $h$-Regular $\Gamma$-Hemiring in terms of Cubic $h$-Ideals. Communications in Advanced Mathematical Sciences. 2020;3(4):218-24.

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