| 释义 |
- Notes
- References
{{Orphan|date=August 2017}}In lattice theory, a mathematical discipline, a finite lattice is slim if no three join-irreducible elements form an antichain.[1] Every slim lattice is planar. A finite planar semimodular lattice is slim if and only if it contains no cover-preserving diamond sublattice M3 (this is the original definition of a slim lattice due to George Grätzer and Edward Knapp).[2] Notes1. ^{{harvtxt|Czédli|Schmidt|2012}}
2. ^{{harvtxt|Grätzer|Knapp|2007}}
References - {{cite book | mr=3495851 | last=Grätzer | first=George| authorlink=George_Grätzer | title=The congruences of a finite lattice. A "proof-by-picture" approach | edition=2nd | publisher=Birkhäuser/Springer | location = Cham, Switzerland | year=2016 | isbn=978-3-319-38796-3 | ref = harv | doi = 10.1007/978-3-319-38798-7}}
- {{cite paper | mr=2380059 | last1=Grätzer | first1=George| authorlink1=George_Grätzer | last2=Knapp | first2=Edward | title= Notes on planar semimodular lattices. I. Construction | journal = Acta Sci. Math. (Szeged) | volume=73 | number = 3–4 | pages = 445–462 | year=2007 | ref = harv }}
- {{cite paper | mr=2979644 | last1=Czédli | first1=Gábor| last2=Schmidt | first2=E. Tamás | title= Slim semimodular lattices. I. A visual approach| journal = Order | volume=29 | number = 3 | pages = 481–497 | year=2012 | ref = harv | url = http://www.math.u-szeged.hu/~czedli/publ.pdf/czedli-schmidt_slim-semimodular-lattices-I.pdf | doi = 10.1007/s11083-011-9215-3 }}
{{algebra-stub}} 1 : Lattice theory |