EN
A note on distributivity of the lattice of $L$-ideals of a ring
Abstract
Many studies have investigated the lattice of fuzzy substructures of algebraic structures such as groups and rings. In this study, we prove that the lattice of $L$-ideals of a ring is distributive if and only if the lattice of its ideals is distributive, for an infinitely $\vee$-distributive lattice $L$.
Keywords
References
- N. Ajmal and K.V. Thomas, The lattices of fuzzy subgroups and fuzzy normal subgroups, Inform. Sci. 76, 1–11, 1994.
- N. Ajmal and K.V. Thomas, The lattice of fuzzy ideals of a ring, Fuzzy Sets and Systems 74, 371–379, 1995.
- N. Ajmal and K.V. Thomas, The lattices of fuzzy normal subgroups is modular, Inform. Sci. 83, 199–218, 1995.
- D. Bayrak and S. Yamak, The lattice of generalized normal L-subgroups, J. Intell. Fuzzy Syst. 27, 1143–1152, 2014.
- D. Bayrak and S. Yamak Distributivity and pseudocomplementation of lattices of generalized L-subgroups, Int. J. Algebra Stat. 5, 107–114, 2016.
- G. Birhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ., Rhode Island, 1967.
- N. Gao, Q. Li and Z. Li, When do L-fuzzy ideals of a ring generate a distributive lattice?, Open Math. 4 (1), 531–542, 2016.
- J.A. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 18, 145–174, 1967.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Publication Date
February 1, 2019
Submission Date
March 14, 2013
Acceptance Date
October 18, 2017
Published in Issue
Year 2019 Volume: 48 Number: 1
APA
Bayrak, D., & Yamak, S. (2019). A note on distributivity of the lattice of $L$-ideals of a ring. Hacettepe Journal of Mathematics and Statistics, 48(1), 180-185. https://izlik.org/JA37YM69JL
AMA
1.Bayrak D, Yamak S. A note on distributivity of the lattice of $L$-ideals of a ring. Hacettepe Journal of Mathematics and Statistics. 2019;48(1):180-185. https://izlik.org/JA37YM69JL
Chicago
Bayrak, Dilek, and Sultan Yamak. 2019. “A Note on Distributivity of the Lattice of $L$-Ideals of a Ring”. Hacettepe Journal of Mathematics and Statistics 48 (1): 180-85. https://izlik.org/JA37YM69JL.
EndNote
Bayrak D, Yamak S (February 1, 2019) A note on distributivity of the lattice of $L$-ideals of a ring. Hacettepe Journal of Mathematics and Statistics 48 1 180–185.
IEEE
[1]D. Bayrak and S. Yamak, “A note on distributivity of the lattice of $L$-ideals of a ring”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 1, pp. 180–185, Feb. 2019, [Online]. Available: https://izlik.org/JA37YM69JL
ISNAD
Bayrak, Dilek - Yamak, Sultan. “A Note on Distributivity of the Lattice of $L$-Ideals of a Ring”. Hacettepe Journal of Mathematics and Statistics 48/1 (February 1, 2019): 180-185. https://izlik.org/JA37YM69JL.
JAMA
1.Bayrak D, Yamak S. A note on distributivity of the lattice of $L$-ideals of a ring. Hacettepe Journal of Mathematics and Statistics. 2019;48:180–185.
MLA
Bayrak, Dilek, and Sultan Yamak. “A Note on Distributivity of the Lattice of $L$-Ideals of a Ring”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 1, Feb. 2019, pp. 180-5, https://izlik.org/JA37YM69JL.
Vancouver
1.Dilek Bayrak, Sultan Yamak. A note on distributivity of the lattice of $L$-ideals of a ring. Hacettepe Journal of Mathematics and Statistics [Internet]. 2019 Feb. 1;48(1):180-5. Available from: https://izlik.org/JA37YM69JL