A note on distributivity of the lattice of $L$-ideals of a ring

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Hacettepe Journal of Mathematics and Statistics
Volume:48 Issue:1
A note on distributivity of the lattice of $L$-ideals of a ring

A note on distributivity of the lattice of $L$-ideals of a ring

Authors : Dilek BAYRAK, Sultan YAMAK

Pages : 180-185

View : 26 | Download : 12

Publication Date : 2019-02-01

Article Type : Research Paper

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 : lattice, distributive lattice, fuzzy ideal

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