Tight Lattice
المؤلف:
Grätzer, G
المصدر:
General Lattice Theory, 2nd ed. Boston, MA: Birkhäuser, 1998.
الجزء والصفحة:
...
2-1-2022
1653
Tight Lattice
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, ![<span style=]()
{(a,b)|a,b in L}" src="https://mathworld.wolfram.com/images/equations/TightLattice/Inline9.gif" style="height:15px; width:94px" />.
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.
الاكثر قراءة في نظرية المجموعات
اخر الاخبار
اخبار العتبة العباسية المقدسة
