Kyungpook Mathematical Journal

  • 제55권3호
  • /
  • Pages.515-530
  • /
  • 2015
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

Characterization of Additive (m, n)-Semihyperrings

  • 투고 : 2013.11.09
  • 심사 : 2014.08.21
  • 발행 : 2015.09.23
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We say that (R, f, g) is an additive (m, n)-semihyperring if R is a non-empty set, f is an m-ary associative hyperoperation, g is an n-ary associative operation and g is distributive with respect to f. In this paper, we describe a number of characterizations of additive (m, n)-semihyperrings which generalize well-known results. Also, we consider distinguished elements, hyperideals, Rees factors and regular relations. Later, we give a natural method to derive the quotient (m, n)-semihyperring.

키워드

참고문헌

  1. S. M. Anvariyeh, S. Mirvakili and B. Davvaz, Fundamental relation on (m, n)-ary hypermodules on (m, n)-ary hyperring, ARS Combinatoria, 94(2010), 273-288.
  2. G. Crombez, On (n, m)-rings, Abh. Math. Semin. Univ. Hamburg, 37(1972), 180-199. https://doi.org/10.1007/BF02999695
  3. G. Crombez and J. Timm, On (n, m)-quotient rings, Abh. Math. Semin. Univ. Hamburg, 37(1972), 200-203. https://doi.org/10.1007/BF02999696
  4. M. R. Darafsheh and B. Davvaz, $H_v$-ring of fractions, Ital. J. Pure Appl. Math., 5(1999), 25-34.
  5. B. Davvaz, Approximations in n-ary algebraic systems, Soft Computing, 12(2008), 409-418.
  6. B. Davvaz, S. Mirvakili, Hyperideals in ternary semihyperrings, Bulletin of the Allahabad Mathematical Society (BAMS), 27(2)(2012), 159-185.
  7. B. Davvaz, V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, 2007.
  8. B. Davvaz and A. Salasi, A realization of hyperrings, Comm. Algebra, 34 (2006), 4389-4400. https://doi.org/10.1080/00927870600938316
  9. B. Davvaz and T. Vougiouklis, n-ary hypergroups, Iran. J. Sci. Tec., Tran. A., 30(2006), 165-174.
  10. B. Davvaz, W. A. Dudek and S. Mirvakili, Neutral elements, fundamental relations and n-ary hypersemigroups, International Journal of Algebra and Computation, 19(2009), 567-583. https://doi.org/10.1142/S0218196709005226
  11. B. Davvaz, W.A. Dudek and T. Vougiouklis, A generalization of n-ary algebraic systems, Comm. Algebra, 37(2009), 1248-1263. https://doi.org/10.1080/00927870802466835
  12. W. Dornte, Untersuchungen uber einen verallgemeinerten Gruppenbegriff, Math. Z., 29(1928), 1-19.
  13. W. A. Dudek On the divisibility theory in (m, n)-rings, Demonstratio Math., 14(1981), 19-32.
  14. M. Ghadiri, B. N. Waphare and B. Davvaz, n-Ary $H_v$-Structures, Southeast Asian Bulletin of Mathematics, 34(2010), 243-255.
  15. E. Kasner, An extension of the group concept, Bull. Amer. Math. Soc., 10(1904), 290-291.
  16. M. Krasner, A class of hyperrings and hyperfields, Int. J. Math. and Math. Sci., 2(1983), 307-312.
  17. S.-M. Lee, On the quotient (${\Omega}$, m)-ringoids, Publ. Inst. Math. (Beograd) (N. S.), 46(60)(1989), 20-24.
  18. V. Leoreanu-Fotea, Several types of n-ary subhypergroups Ital. J. Pure Appl. Math., 23(2008), 261-274.
  19. V. Leoreanu-Fotea, n-ary canonical hypergroups, Ital. J. Pure Appl. Math., 24(2008), 247-254.
  20. V. Leoreanu-Fotea and B. Davvaz, Join n-spaces and lattices, Journal Multiple-valued Logic and Soft Computing, 15(2009), 421-432.
  21. V. Leoreanu-Fotea and B. Davvaz, Roughness in n-ary hypergroups, Information Sciences, 178(2008), 4114-4124. https://doi.org/10.1016/j.ins.2008.06.019
  22. F. Marty, Sur une generalization de la notation de grouse 8th Congress, Math. Scandianaves, Stockholm, 1934, pp. 45-49.
  23. S. Mirvakili and B. Davvaz, Relations on Krasner (m, n)-hyperrings, European J. Combin., 31(2010), 790-802. https://doi.org/10.1016/j.ejc.2009.07.006
  24. J. Mittas, Hypergroupes canoniques, Math. Balkanica, Beograd, 2(1972), 165-179.
  25. E. L. Post, Polyadic groups, Trans. Amer. Math. Soc., 48(1940), 208-350. https://doi.org/10.1090/S0002-9947-1940-0002894-7
  26. S. A. Rusakov, Some applications of n-ary group theory, Belaruskaya navuka, Minsk, 1998.