Distributive lattices with strong endomorphism kernel property as direct sums
Unbounded distributive lattices which have strong endomorphism kernel property (SEKP) introduced by Blyth and Silva in [3] were fully characterized in [11] using Priestley duality (see Theorem 2.8}). We shall determine the structure of special elements (which are introduced after Theorem 2.8 under...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2020-07-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | https://cgasa.sbu.ac.ir/article_87512_30a0285f83407ee46e5bc8449eb777a0.pdf |
| Summary: | Unbounded distributive lattices which have strong endomorphism kernel property (SEKP) introduced by Blyth and Silva in [3] were fully characterized in [11] using Priestley duality (see Theorem 2.8}). We shall determine the structure of special elements (which are introduced after Theorem 2.8 under the name strong elements) and show that these lattices can be considered as a direct product of three lattices, a lattice with exactly one strong element, a lattice which is a direct sum of 2 element lattices with distinguished elements 1 and a lattice which is a direct sum of 2 element lattices with distinguished elements 0, and the sublattice of strong elements is isomorphic to a product of last two mentioned lattices. |
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| ISSN: | 2345-5853 2345-5861 |