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Generalized Derivations of Hyperlattices

Year 2019, Volume: 40 Issue: 2, 299 - 304, 30.06.2019

Seda Oğuz Ünal , Hasret Durna

https://doi.org/10.17776/csj.414343
https://izlik.org/JA36JZ84ET

Abstract

In this paper the notion of generalized derivation for
a hyperlattice is introduced and some basic properties of them are derived.

Keywords

Generalized derivations Hyperlattice

References

  • [1] F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934) 45–49.
  • [2] R. Ameri, M. Norouzi, New fundamental relation of hyperrings, European J. Combin. 34 (5) (2013) 884–891.
  • [3] P. Corsini, V. Leoreanu, Applications of Hyperstructure Theory, Kluwer Academic Publishers, Dordrecht (2003).
  • [4] J. Jantosciak, Transposition hypergroups: noncommutative join spaces. J. Algebra 187(1) (1997) 97–119.
  • [5] J. Zhan, B. Davvaz, P. K. Shun, Probability n-arybypergroups, Information Science 180 (2010) 1159–1166.
  • [6] R. Rosaria. Hyperaffine planes over hyperrings, Discrete Math. 155(1-3)(1996) 215–223.
  • [7] J. Zhan, C. Irina,Γ-hypermodules:isomorphism theorems and regularrelations, U.P.B. Sci Bull, Ser. A 73 (2011) 71–78.
  • [8] M. Konstantinidou, J. Mittas. An introduction to the theory of hyperlattices. Math. Balkanica,1977, 7: 187–193.
  • [9] Mittas, M. Konstantinidou, Sur unenouvellegeneration de la notion de treillis,Lessupertreilliset certaines de leursproprietiesgenerales,AnnSciUnivBlaise Pascal Ser Math, 25 (1989) 61–83.
  • [10] Xiaozhi Guo, Xiaolong Xin, Hyperlattices, Pure and Applied Mathematics (Xi’an) 20 (2004) 40–43.
  • [11] A. Rahnami-Barghi. The prime ideal theorem for distributive hyperlattices. Ital. J. Pure Appl. Math 10 (2001) 75–78.
  • [12] S. Rasouli, B. Davvaz, Construction and spectral topology on hyperlattices. Mediterr. J. Math.,7(2) (2010) 249–262.
  • [13] S. Rasouli, B. Davvaz, Lattices derived from hyperlattices, Commun. Algebra 38 (8) (2010) 2720–2737.
  • [14] H. E. Bell, G. Mason,Derivation in Near-Rings, North-Holland Math. Stud., North-Holland, Amsterdam 137 (1987).
  • [15] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8(1957) 1093–1100.
  • [16] M. Bresar, On the distance of composition of the two derivations to the generalized derivations, Glasgow math. J., 33(1), (1991), 89-93.
  • [17] N. O. Alshehri, Generalized derivations of lattices, Int. J. Contemp. Math. Sciences, 5 (13) (2010) 629-640.
  • [18] J. Wang, Y. Jun, Xiaolong Xin, Y. Zou, On derivations of bounded hyperlattices, Journal of Mathematical Research and Applications 36(2) (2016) 151-161.

Hiperlatisler Üzerinde Genelleştirilmiş Türevler

Year 2019, Volume: 40 Issue: 2, 299 - 304, 30.06.2019

Seda Oğuz Ünal , Hasret Durna

https://doi.org/10.17776/csj.414343
https://izlik.org/JA36JZ84ET

Abstract

Bu makalede hiperlatisler üzerinde genelleştirilmiş türev kavramı
tanıtıldı ve bunların bazı temel özellikleri elde edildi. 

Keywords

Genelleştirilmiş türevler Hiperlatis

References

  • [1] F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934) 45–49.
  • [2] R. Ameri, M. Norouzi, New fundamental relation of hyperrings, European J. Combin. 34 (5) (2013) 884–891.
  • [3] P. Corsini, V. Leoreanu, Applications of Hyperstructure Theory, Kluwer Academic Publishers, Dordrecht (2003).
  • [4] J. Jantosciak, Transposition hypergroups: noncommutative join spaces. J. Algebra 187(1) (1997) 97–119.
  • [5] J. Zhan, B. Davvaz, P. K. Shun, Probability n-arybypergroups, Information Science 180 (2010) 1159–1166.
  • [6] R. Rosaria. Hyperaffine planes over hyperrings, Discrete Math. 155(1-3)(1996) 215–223.
  • [7] J. Zhan, C. Irina,Γ-hypermodules:isomorphism theorems and regularrelations, U.P.B. Sci Bull, Ser. A 73 (2011) 71–78.
  • [8] M. Konstantinidou, J. Mittas. An introduction to the theory of hyperlattices. Math. Balkanica,1977, 7: 187–193.
  • [9] Mittas, M. Konstantinidou, Sur unenouvellegeneration de la notion de treillis,Lessupertreilliset certaines de leursproprietiesgenerales,AnnSciUnivBlaise Pascal Ser Math, 25 (1989) 61–83.
  • [10] Xiaozhi Guo, Xiaolong Xin, Hyperlattices, Pure and Applied Mathematics (Xi’an) 20 (2004) 40–43.
  • [11] A. Rahnami-Barghi. The prime ideal theorem for distributive hyperlattices. Ital. J. Pure Appl. Math 10 (2001) 75–78.
  • [12] S. Rasouli, B. Davvaz, Construction and spectral topology on hyperlattices. Mediterr. J. Math.,7(2) (2010) 249–262.
  • [13] S. Rasouli, B. Davvaz, Lattices derived from hyperlattices, Commun. Algebra 38 (8) (2010) 2720–2737.
  • [14] H. E. Bell, G. Mason,Derivation in Near-Rings, North-Holland Math. Stud., North-Holland, Amsterdam 137 (1987).
  • [15] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8(1957) 1093–1100.
  • [16] M. Bresar, On the distance of composition of the two derivations to the generalized derivations, Glasgow math. J., 33(1), (1991), 89-93.
  • [17] N. O. Alshehri, Generalized derivations of lattices, Int. J. Contemp. Math. Sciences, 5 (13) (2010) 629-640.
  • [18] J. Wang, Y. Jun, Xiaolong Xin, Y. Zou, On derivations of bounded hyperlattices, Journal of Mathematical Research and Applications 36(2) (2016) 151-161.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Seda Oğuz Ünal 0000-0003-1338-1466

Hasret Durna 0000-0002-9987-2970

Submission Date April 11, 2018
Acceptance Date March 4, 2019
Publication Date June 30, 2019
DOI https://doi.org/10.17776/csj.414343
IZ https://izlik.org/JA36JZ84ET
Published in Issue Year 2019 Volume: 40 Issue: 2

Cite

APA Oğuz Ünal, S., & Durna, H. (2019). Generalized Derivations of Hyperlattices. Cumhuriyet Science Journal, 40(2), 299-304. https://doi.org/10.17776/csj.414343

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