Fully invariant and verbal congruence relations

Date
2013-01-01
Authors
Bergman, Clifford
Berman, Joel
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Mathematics
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Abstract

A congruence relation θ on an algebra A is fully invariant if every endomorphism of A preserves θ. A congruence θ is verbal if there exists a variety V such that θ is the least congruence of A such that A/θ ∈ V. Every verbal congruence relation is known to be fully invariant. This paper investigates fully invariant congruence relations that are verbal, algebras whose fully invariant congruences are verbal, and varieties for which every fully invariant congruence in every algebra in the variety is verbal.

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This is a post-peer-review, pre-copyedit version of an article published in Algebra universalis. The final authenticated version is available online at DOI: 10.1007/s00012-013-0238-z. Posted with permission.

Keywords
verbal congruence, fully invariant congruence, verbose
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