Congruences

George Grätzer ()
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George Grätzer: University of Manitoba, Department of Mathematics

Chapter Chapter III in Lattice Theory: Foundation, 2011, pp 207-254 from Springer

Abstract: Abstract In Section I.3.6, we saw that x ≡ y (mod _) iff x ^ y ≡ x ≡ y (modα); therefore, to investigate how congruences spread, it is enough to deal with comparable pairs, a ≤b and c ≤ d. By Lemma 10, the congruence blocks are convex sublattices, so instead of comparable pairs, we shall deal with intervals [a; b] and [c; d].

Keywords: Congruence Relation; Congruence Lattice; Neutral Element; Modular Lattice; Standard Ideal (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-3-0348-0018-1_3

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