CLOSURE OPERATOR AND α-IDEALS IN 0-DISTRIBUTIVE LATTICES 


By

S. S. Khopade¹ , S. P. Thorat² and Laxmi Rathour³ 

¹Karmaveer Hire Arts, Science, Commerce and Education College, Gargoti, Maharashtra, India-416209 

²Vivekanand College (Empowered Autonomous), Kolhapur, Maharashtra, India-416003 

³Department of Mathematics, National Institute of Technology, Chaltlang, Aizawl, Mizoram, India-796012 

Email: santajikhopade@gmail.com, thoratsanjay15@gmail.com, laxmirathour817@gmail.com

 (Received: October 08, 2024; In format: October 29, 2024; Revised: June 09, 2024; Accepted: June 10, 2024) 


DOI: https://doi.org/10.58250/jnanabha.2024.54138 



Abstract

A closure operator on the lattice of all ideals of a bounded 0-distributive lattice is introduced. It is observed that the ideals which are closed with respect to this closure operator are α-ideals in it and conversely. 


2020 Mathematical Sciences Classification: 06D75. 

Keywords and Phrases: 0- distributive lattice, ideal, closure operator, homomorphism, α-ideal 

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