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Thread: Congruence extension property (CEP)

  1. #1 Congruence extension property (CEP) 
    New Member
    Join Date
    Jan 2014
    I have this problem to solve and I have no idea how to do it...

    Show that the class of Abelian groups has the CEP. Does the class of lattices have the CEP?

    An algebra A has the congruence extension property (CEP) if for every and there is a such that . A class K of algebras has the CEP if every algebra in the class has the CEP.

    How can I solve this?
    Thanks for all your hints.

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  3. #2  
    Forum Professor river_rat's Avatar
    Join Date
    Jun 2006
    South Africa
    For groups, congruences correspond to normal subgroups and for abelian groups every subgroup is normal. That should be enough to show the first question.

    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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