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Date: 17-1-2022
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Date: 27-12-2021
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Date: 17-1-2022
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Let be a nontrivial bounded lattice (or a complemented lattice, etc.). Then is a tight lattice if every proper tolerance of satisfies
Tight lattices play an important role in the study of congruence lattices on finite algebras. One can show that a finite lattice is tight if and only if it is -simple and every strictly increasing meet endomorphism of is constant. One can also show that a finite lattice is tight if and only if its only connected tolerance is the all relation, .
REFERENCES:
Grätzer, G. General Lattice Theory, 2nd ed. Boston, MA: Birkhäuser, 1998.
Hobby, D. and McKenzie, R. The Structure of Finite Algebras. Providence, RI: Amer. Math. Soc., 1988.
Insall, M. "Some Finiteness Conditions in Lattices Using Nonstandard Proof Methods." J. Austral. Math. Soc. 53, 266-280, 1992.
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كيف تساهم الأطعمة فائقة المعالجة في تفاقم مرض يصيب الأمعاء؟
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مشروع ضخم لإنتاج الهيدروجين الأخضر يواجه تأخيرًا جديدًا
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المجمع العلمي يختتم دورته القرآنية في فن الصوت والنغم بالطريقة المصرية
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