Distributive lattices with strong endomorphism kernel property as direct sums | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 4، دوره 13، شماره 1، مهر 2020، صفحه 45-54 اصل مقاله (412.36 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.29252/cgasa.13.1.45 | ||
| نویسنده | ||
| Jaroslav Gurican | ||
| Department of Algebra and Geometry, Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava, Slovakia. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Unbounded distributive lattice؛ strong endomorphism kernel property؛ congruence relation؛ bounded Priestley space؛ Priestley duality؛ strong element؛ direct sum | ||
| مراجع | ||
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