본문 바로가기
KERD
논문KCI 등재

$L$-fuzzy prime ideals and maximal $L$-fuzzy ideals of a poset

Berhanu Assaye Alaba|Derso Abeje Engidaw|Mihret Alamneh Taye
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2019.08|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제18권 제1호|pp. 1-13|DOI 10.30948/afmi.2019.18.1.1

1

조회

0

다운로드

1

인용

0

참고문헌

키워드

PosetL-fuzzy idealL-fuzzy prime idealPrime L-fuzzy idealMaximal L-fuzzy ideal

초록

In this paper we introduce the notions of $L$-fuzzy prime ideals, prime and maximal $L$-fuzzy ideals of a poset. We also study and establish some characterizations of them and give sufficient conditions for the existence of prime $L$-fuzzy ideals in the lattice of all $L$-fuzzy ideals of a poset.

Abstract

In this paper we introduce the notions of $L$-fuzzy prime ideals, prime and maximal $L$-fuzzy ideals of a poset. We also study and establish some characterizations of them and give sufficient conditions for the existence of prime $L$-fuzzy ideals in the lattice of all $L$-fuzzy ideals of a poset.

참고문헌 (21)

  1. Berhanu Assaye Alaba, "L-fuzzy ideals of a poset", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 16(3), pp.285~299 (2018), 기초자연과학연구소[DOI]
  2. G. Birkhoof, "Lattice theory", Amer. Math. Soc. Colloquium publications, 24 (1967)
  3. B. A. Davey, "Introduction to lattices and order" (1990), Cambridge Univ. Press
  4. M. Erne, "Prime and maximal ideals of partially ordered sets", Math. Slovaca, 56(1), pp.1~22 (2006)
  5. M. Erne, "Ideals in atomic posets", Discrete Mathematics, 338, pp.954~971 (2015)
  6. J. A. Goguen, "L-fuzzy sets", J. Math. Anal. Appl, 18, pp.145~174 (1967)
  7. G.Gratzer, "General lattice theory" (1978), Academic Press
  8. R. Halas, "Annihilators and ideals in ordered sets", Czechoslovak Math. J, 45(120), pp.127~134 (1995)
  9. R. Halas, "Polars and prime ideals in ordered sets. Discuss. Math", Algebra and Stochastic Methods, 15, pp.43~59 (1995)
  10. V. Joshi, "Prime ideals in 0-distributive posets", Cent Eur J. Math, 11(5), pp.940~955 (2013)
  11. V. S. Kharat, "Primeness and semiprimeness in posets", Math. Bohem, 134(1), pp.19~30 (2009)
  12. B. B. N. Koguep, "On fuzzy prime ideals of lattices", SJPAM, 3, pp.1~11 (2008)
  13. J. N. Mordeson, "Fuzzy commutative algebra" (1998), World Sci. Publ
  14. A. Rosenfeld, "Fuzzy groups", J. Math. Anal. Appl, 35, pp.512~517 (1971)
  15. M. H. Stone, "The theory of representations for boolean algebras", Trans. Amer. Math. Soc, 40, pp.37~111 (1936)
  16. K. L. N. Swamy, "Fuzzy prime ideals of rings", J. Math. Anal. and Appl, 134, pp.94~103 (1988)
  17. U. M. Swamy, "Fuzzy ideals and congruences of lattices", Fuzzy Sets and Systems, 95, pp.249~253 (1998)
  18. U. M. Swamy, "Algebraic fuzzy systems", Fuzzy Sets and Systems, 41, pp.187~194 (1991)
  19. U. M. Swamy, "Irreducibility in algebraic fuzzy systems", Fuzzy Sets and Systems, 41, pp.233~241 (1991)
  20. C. K.Wong, "Fuzzy point and local properties of fuzzy topology", J. Math. Anal. Appl, 46, pp.316~328 (1974)
  21. L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)

관련 논문AI추천

L-fuzzy ideals of a posetBerhanu Assaye Alaba, Derso Abeje Engidaw, Miheret Alamneh Taye기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2018 · 제16권 제3호ON L-FUZZY SEMI-PRIME IDEALS OF A POSET AND SEPARATION THEOREMSDerso Abeje Engidaw, Tilahun Bimerew Alemu강원경기수학회 · 한국수학논문집2021 · 제29권 제2호Prime $L$-fuzzy filters of a semilatticeB. Subrahmanyam, Ch. Santhi Sundar Raj, U. M. Swamy기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2020 · 제20권 제1호α-fuzzy ideals and space of prime α-fuzzy ideals in distributive latticesBerhanu Assaye Alaba, Wondwosen Zemene Norahun기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2019 · 제17권 제2호$L$-fuzzy semi-prime ideals in universal algebrasBerhanu Assaye Alaba, Gezahagne Mulat Addis강원경기수학회 · 한국수학논문집2019 · 제27권 제2호zJ− Ideals and Strongly Prime Ideals in PosetsBalasubramanian Elavarasan, Catherine Grace John경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2017 · 제57권 제3호

이 간행물의 다른 논문 (6건)

Inverse int-fuzzy soft bi-ideals over semigroupsPeerapong Suebsanpp. 15-30Quasi-interior ideals and fuzzy quasi-interior ideals of $\Gamma$-semiringsMarapureddy Murali Krishna Raopp. 31-43Rough approximations on $L$-groupsXueyou Chenpp. 45-55The category of hesitant $H$-fuzzy sets임평기, 전영배, 이정곤, 허걸, 김준희pp. 57-74New separation axioms in soft topological spaceA.R. Prasannan, Jayanta Biswaspp. 75-91
원문 보기