Localizations of topologies on distributive lattices (in Ukrainian) |
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| Author | |
| Abstract |
In this paper the bounded distributive
lattices with local defined topologies (pre topologies) are introduced and
described. The results
are completely similar to that of the~author, W.~Brandal and
E.~Barbut for commutative rings. It is shown that the~lattice of
subsets of infinite set with finite complements is an~adequate
model of the~introduced notions.
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| Keywords |
bounded distributive lattices, local topologies, pretopologies, lattice of subsets, infinite set, finite complements, commutative rings
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| DOI |
doi:10.30970/ms.8.2.180-188
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Reference |
1. Brandal W., Barbut E. Localizations of torsion theories. Pacific J. Math., 1983, vol. 107, no. 1, pp. 27–37.
2. Georgescu G. $\frak F$-multipliers and the localization of distributive lattices. Algebra Universalis, 1985, vol. 21, pp. 181–197. 3. Georgescu G. $\frak F$-local distributive lattices. Math. Japonica, 1990, vol. 35, no. 5, pp. 909–916. 4. Brezuleanu A., Diaconescu R. Sur la duale de la catégorie des treillies. Rev. Roum. Math. Pures et Appl., vol. XIY, no. 3 (1969), pp. 311–323. 5. Тушницкий И.Я. Кольца с локально определенными кручениями. Алгебра и логика, 1991, т. 30, №3, с. 369–377. 6. Тушницький І.Я. Кільця з локально визначеними крученнями. Тематичний збірник наукових праць "Алгебра і топологія", Київ, 1993, с. 88–109. 7. Тушницкий И.Я. О локализациях решеток. Алгебра и анализ. Тезисы докладов международной конференции памяти Н. Чеботарева, ч. 1, Казань, 1994, с. 94. |
| Pages |
180-188
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| Volume |
8
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| Issue |
2
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| Year |
1997
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |