Magic Wands

George Grätzer

Chapter Chapter 18 in The Congruences of a Finite Lattice, 2016, pp 201-222 from Springer

Abstract: Abstract A typical way of constructing an algebra B with a given congruence lattice C is to construct an algebra A with a much larger congruence lattice and then “collapsing” sufficiently many pairs of congruences of the form con ( a , b ) $$\text{con}(a,b)$$ and con ( c , d ) $$\text{con}(c,d)$$ in B, so that the congruence lattice “shrinks” to C. To do this we need a “magic wand” that will make a ≡ b $$a \equiv b$$ equivalent to c ≡ d $$c \equiv d$$ .

Keywords: Magic Wand; Congruence Lattice; Congruence-preserving Extension; Partial Unary Operation; Final Glue (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-38798-7_18

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