Maximal Ideal and Prime Ideal in an L-lattice
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...
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Tsinghua University Press
2024-09-01
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| Series: | Fuzzy Information and Engineering |
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| Online Access: | https://www.sciopen.com/article/10.26599/FIE.2024.9270044 |
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| author | Aparna Jain Iffat Jahan |
| author_facet | Aparna Jain Iffat Jahan |
| author_sort | Aparna Jain |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-15c7fc3b80be460191f0d06fcbe0ba43 |
| institution | Kabale University |
| issn | 1616-8658 1616-8666 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj-art-15c7fc3b80be460191f0d06fcbe0ba432024-11-29T02:03:23ZengTsinghua University PressFuzzy Information and Engineering1616-86581616-86662024-09-0116324426310.26599/FIE.2024.9270044Maximal Ideal and Prime Ideal in an L-latticeAparna Jain0Iffat Jahan1Department of Mathematics, Shivaji College, University of Delhi, New Delhi 110027, IndiaDepartment of Mathematics, Ramjas College, University of Delhi, Delhi 110007, IndiaIn 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.https://www.sciopen.com/article/10.26599/FIE.2024.9270044latticesl-sublattice, l-ideall-dual ideall-maximal ideall-prime ideal |
| spellingShingle | Aparna Jain Iffat Jahan Maximal Ideal and Prime Ideal in an L-lattice Fuzzy Information and Engineering lattices l-sublattice, l-ideal l-dual ideal l-maximal ideal l-prime ideal |
| title | Maximal Ideal and Prime Ideal in an L-lattice |
| title_full | Maximal Ideal and Prime Ideal in an L-lattice |
| title_fullStr | Maximal Ideal and Prime Ideal in an L-lattice |
| title_full_unstemmed | Maximal Ideal and Prime Ideal in an L-lattice |
| title_short | Maximal Ideal and Prime Ideal in an L-lattice |
| title_sort | maximal ideal and prime ideal in an l lattice |
| topic | lattices l-sublattice, l-ideal l-dual ideal l-maximal ideal l-prime ideal |
| url | https://www.sciopen.com/article/10.26599/FIE.2024.9270044 |
| work_keys_str_mv | AT aparnajain maximalidealandprimeidealinanllattice AT iffatjahan maximalidealandprimeidealinanllattice |