Disjunctive Ideals of Almost Distributive Lattices
The concept of disjunctive ideals is introduced in an Almost Distributive Lattice (ADL). It is proved that the set of all disjunctive ideals of an ADL forms a complete lattice. A necessary and sufficient condition is derived for an inverse homomorphic image of a disjunctive ideal of an ADL to be aga...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2022-03-01
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| Series: | Discussiones Mathematicae - General Algebra and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgaa.1384 |
| _version_ | 1797705831475576832 |
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| author | Rafi N. Srujana M. Rao T. Srinivasa |
| author_facet | Rafi N. Srujana M. Rao T. Srinivasa |
| author_sort | Rafi N. |
| collection | DOAJ |
| description | The concept of disjunctive ideals is introduced in an Almost Distributive Lattice (ADL). It is proved that the set of all disjunctive ideals of an ADL forms a complete lattice. A necessary and sufficient condition is derived for an inverse homomorphic image of a disjunctive ideal of an ADL to be again a disjunctive ideal. Later, the concept of strongly disjunctive ideals is introduced in an ADL and their properties are studied. Some equivalent conditions are established for the set of all strongly disjunctive ideals to convert into a sublattice of the ideal lattice. |
| first_indexed | 2024-03-12T05:43:12Z |
| format | Article |
| id | doaj.art-1a6a853ebcfe4065bf9608282735decc |
| institution | Directory Open Access Journal |
| issn | 2084-0373 |
| language | English |
| last_indexed | 2024-03-12T05:43:12Z |
| publishDate | 2022-03-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae - General Algebra and Applications |
| spelling | doaj.art-1a6a853ebcfe4065bf9608282735decc2023-09-03T05:51:42ZengUniversity of Zielona GóraDiscussiones Mathematicae - General Algebra and Applications2084-03732022-03-0142115917810.7151/dmgaa.1384Disjunctive Ideals of Almost Distributive LatticesRafi N.0Srujana M.1Rao T. Srinivasa2Department of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh, India-522 101Department of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh, India-522 101Department of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh, India-522 101The concept of disjunctive ideals is introduced in an Almost Distributive Lattice (ADL). It is proved that the set of all disjunctive ideals of an ADL forms a complete lattice. A necessary and sufficient condition is derived for an inverse homomorphic image of a disjunctive ideal of an ADL to be again a disjunctive ideal. Later, the concept of strongly disjunctive ideals is introduced in an ADL and their properties are studied. Some equivalent conditions are established for the set of all strongly disjunctive ideals to convert into a sublattice of the ideal lattice.https://doi.org/10.7151/dmgaa.1384almost distributive lattice (adl)normal adldisjunctive idealstrongly disjunctive idealnormal prime idealminimal prime ideal06d9906d15 |
| spellingShingle | Rafi N. Srujana M. Rao T. Srinivasa Disjunctive Ideals of Almost Distributive Lattices Discussiones Mathematicae - General Algebra and Applications almost distributive lattice (adl) normal adl disjunctive ideal strongly disjunctive ideal normal prime ideal minimal prime ideal 06d99 06d15 |
| title | Disjunctive Ideals of Almost Distributive Lattices |
| title_full | Disjunctive Ideals of Almost Distributive Lattices |
| title_fullStr | Disjunctive Ideals of Almost Distributive Lattices |
| title_full_unstemmed | Disjunctive Ideals of Almost Distributive Lattices |
| title_short | Disjunctive Ideals of Almost Distributive Lattices |
| title_sort | disjunctive ideals of almost distributive lattices |
| topic | almost distributive lattice (adl) normal adl disjunctive ideal strongly disjunctive ideal normal prime ideal minimal prime ideal 06d99 06d15 |
| url | https://doi.org/10.7151/dmgaa.1384 |
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