科研之友
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摘要
In a finite lattice, a congruence spreads from a prime interval to another by a sequence of congruence-perspectivities through intervals of arbitrary size, by a 1955 result of J. Jakubik. In this note, I introduce the concept of prime-perspectivity and prove the Prime-projectivity Lemma: a congruence spreads from a prime interval to another by a sequence of prime-perspectivities through prime intervals. A planar semimodular lattice is slim, if it contains no M (3) sublattice. I introduce the Swing Lemma, a very strong version of the Prime-projectivity Lemma for slim, planar, and semimodular lattices.
- 出版日期2015-11
