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The Structure of Finite Algebras

Author(s): David Hobby and Ralph McKenzie  
Publisher: AMS  
Edition: 1  

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Structure of Finite Algebras (Contemporary Mathematics)

Book Description

The service of agreement lattices in revealing the structure of general algebras has been recognized since Garrett Birkhoff's pioneering work in the 1930s and 1940s. Still, the results presented in this book are of very recent origin: most of them were developed in 1983. The main discovery presented here is that the lattice of congruence of a finite algebra is deeply connected to the structure of that algebra. The theory discloses a sharp division of locally finite varieties of algebras into six interesting new families, each of which is characterized by the behavior of congruence in the algebras. The authors use the theory to derive many new results that will be of interest not only to universal algebraists, but to other algebraists as well.

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