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$d$-fuzzy ideals and injective fuzzy ideals in distributive lattices

Berhanu Assaye Alaba|Mihret Alamneh Taye|Wondwosen Zemene Norahun
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2019.12|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제18권 제3호|pp. 233-243|DOI 10.30948/afmi.2019.18.3.233

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참고문헌

키워드

DerivationFuzzy ideal$d$-idealInjective ideal$d$-fuzzy idealInjective fuzzy ideal

초록

In this paper, we introduce the concept of $d$-fuzzy ideals and injective fuzzy ideals in a distributive lattice with respect to derivation. It is proved that the set of all $d$-fuzzy ideals forms a distributive lattice. A set of equivalent conditions are derived for a derivation $d$ of $L$ to became injective. Moreover, we proved that the set of all injective fuzzy ideals forms a complete distributive lattice.

Abstract

In this paper, we introduce the concept of $d$-fuzzy ideals and injective fuzzy ideals in a distributive lattice with respect to derivation. It is proved that the set of all $d$-fuzzy ideals forms a distributive lattice. A set of equivalent conditions are derived for a derivation $d$ of $L$ to became injective. Moreover, we proved that the set of all injective fuzzy ideals forms a complete distributive lattice.

참고문헌 (17)

  1. Berhanu Assaye Alaba, "Fuzzy annihilator ideals in distributive lattices", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 16(2), pp.191~200 (2018), 기초자연과학연구소[DOI]
  2. Berhanu Assaye Alaba, "α-fuzzy ideals and space of prime α-fuzzy ideals in distributive lattices", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 17(2), pp.147~163 (2019), 기초자연과학연구소[DOI]
  3. H. E. Bell, "Rings in which derivations satisfy certain algebraic conditions", Acta Math. Hungar, 53(3-4), pp.339~346 (1989)
  4. G. Birkho, "Lattice Theory", Amer. Math. Soc. Colloq, XXV (1967)
  5. L. Ferrari, "On derivations of lattices", Pure Mathematics and Applications, 12(45), pp.365~382 (2001)
  6. K. Kaya, "Prime rings with a derivations", Bull. Mater. Sci. Eng, 16, pp.63~71 (1987)
  7. M. Kondo, "On the transfer principle in fuzzy theory", Mathware and Soft Computing, 12, pp.41~55 (2005)
  8. B. B. N. Koguep, "On fuzzy prime ideals of lattices", SJPAM, 3, pp.1~11 (2008)
  9. W. J. Liu, "Fuzzy invariant subgroups and fuzzy ideals", Fuzzy sets and systems, 8, pp.133~139 (1982)
  10. E. Posner, "Derivations in prime rings", Proc. Amer. Math. Soc, 8, pp.1093~1100 (1957)
  11. M. S. Rao, "d-ideals and injective ideals in a distributive lattice", International Journal of Math-ematics and Soft Computing, 2(1), pp.65~73 (2012)
  12. A. Rosenfeld, "Fuzzy Subgroups", J. Math. Anal. Appl, 35, pp.512~517 (1971)
  13. U. M. Swamy, "Fuzzy ideals and congruences of lattices", Fuzzy Sets and Systems, 95, pp.249~253 (1998)
  14. G. Szasz, "Translation der verbande", Acta Fac. Rer. Nat. Univ. Comenianae, 5, pp.53~57 (1961)
  15. G. Szasz, "derivations of lattices", Acta Sci. Math, 37, pp.149~154 (1975)
  16. B. Yuan, "Fuzzy ideals on a distributive lattice", Fuzzy Sets and Systems, 35, pp.231~240 (1990)
  17. L. A. Zadeh, "Fuzzy Sets", Information and Control, 8, pp.338~353 (1965)

관련 논문AI추천

Fuzzy annihilator ideals in distributive latticesBerhanu Assaye Alaba, Wondwosen Zemene Norahun기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2018 · 제16권 제2호α-fuzzy ideals and space of prime α-fuzzy ideals in distributive latticesBerhanu Assaye Alaba, Wondwosen Zemene Norahun기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2019 · 제17권 제2호Fuzzy ideals of almost distributive latticesCh. Santhi Sundar Raj, Natnael Teshale A., U. M. Swamy기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2017 · 제14권 제4호$\sigma$-fuzzy ideals of distributive p-algebrasBerhanu Assaye Alaba, Wondwosen Zemene Norahun기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2019 · 제17권 제3호Fuzzy sublattices of latticesCh. Santhi Sundar Raj, K. Ramanuja Rao, K. Rama Prasad, Natnael Teshale A.기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2019 · 제18권 제2호Fuzzy congruence relations on almost distributive latticesBerhanu Assaye Alaba, Gezahagne Mulat Addis기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2017 · 제14권 제3호

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