Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

2013

Journal or Book Title

Algebra Universalis

Volume

70

Issue

1

First Page

71

Last Page

94

DOI

10.1007/s00012-013-0238-z

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" role="presentation" style="box-sizing: border-box; display: inline-table; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">VV such that θ is the least congruence of Asuch that A/θ∈V" role="presentation" style="box-sizing: border-box; display: inline-table; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">A/θ∈VA/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.

Comments

The final publication is available at Springer via https://doi.org/10.1007/s00012-013-0238-z. Bergman, Clifford, and Joel Berman. "Fully invariant and verbal congruence relations." Algebra Universalis 70, no. 1 (2013): 71-94. Posted with permission.

Copyright Owner

Springer Basel

Language

en

File Format

application/pdf

Published Version

Included in

Algebra Commons

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