1. Maximal Ideal and Prime Ideal in an L-lattice
- Author
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Aparna Jain and Iffat Jahan
- Subjects
lattices ,l-sublattice, l-ideal ,l-dual ideal ,l-maximal ideal ,l-prime ideal ,Engineering (General). Civil engineering (General) ,TA1-2040 ,Mathematics ,QA1-939 - Abstract
In this paper, the notions of an L-sublattice, L-ideal, and L-dual ideal of an L-lattice are introduced. The concepts of an L-maximal ideal and an L-prime ideal in an L-lattice are also defined. The present paper also gives the precise structures of an L-sublattice, L-ideal (dual ideal) generated by an L-subset of an L-lattice. Finally, it is proved that under certain conditions, an L-maximal ideal in an L-lattice is L-prime. It is important to note that, in our studies, the evaluation lattice changes from [0,1] to a lattice L and the parent structure shifts from an ordinary lattice to an L-lattice.
- Published
- 2024
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