Prime Intervals and Congruences

George Grätzer

Chapter Chapter 24 in The Congruences of a Finite Lattice, 2016, pp 291-313 from Springer

Abstract: Abstract As we have discussed in Section 3.2 , to investigate the congruences of a finite lattice L, we should focus on the prime intervals. The congruence-projectivity relation ⇒ is a preordering on Prime ( L ) $$\mathop{\mathrm{Prime}}\nolimits (L)$$ . The equivalence classes under ⇔ $$\Leftrightarrow $$ form an ordered set that is isomorphic to $$\mathop{\mathrm{Con}_{J}} L$$ .

Keywords: Prime Interval; Finite Lattice; Join-irreducible Congruences; Squared Covariance; Planar Semimodular Lattices (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-38798-7_24

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