---
_id: '10864'
abstract:
- lang: eng
  text: We prove that every congruence distributive variety has directed Jónsson terms,
    and every congruence modular variety has directed Gumm terms. The directed terms
    we construct witness every case of absorption witnessed by the original Jónsson
    or Gumm terms. This result is equivalent to a pair of claims about absorption
    for admissible preorders in congruence distributive and congruence modular varieties,
    respectively. For finite algebras, these absorption theorems have already seen
    significant applications, but until now, it was not clear if the theorems hold
    for general algebras as well. Our method also yields a novel proof of a result
    by P. Lipparini about the existence of a chain of terms (which we call Pixley
    terms) in varieties that are at the same time congruence distributive and k-permutable
    for some k.
acknowledgement: The second author was supported by National Science Center grant
  DEC-2011-/01/B/ST6/01006.
article_processing_charge: No
arxiv: 1
author:
- first_name: Alexandr
  full_name: Kazda, Alexandr
  id: 3B32BAA8-F248-11E8-B48F-1D18A9856A87
  last_name: Kazda
- first_name: Marcin
  full_name: Kozik, Marcin
  last_name: Kozik
- first_name: Ralph
  full_name: McKenzie, Ralph
  last_name: McKenzie
- first_name: Matthew
  full_name: Moore, Matthew
  last_name: Moore
citation:
  ama: 'Kazda A, Kozik M, McKenzie R, Moore M. Absorption and directed Jónsson terms.
    In: Czelakowski J, ed. <i>Don Pigozzi on Abstract Algebraic Logic, Universal Algebra,
    and Computer Science</i>. Vol 16. OCTR. Cham: Springer Nature; 2018:203-220. doi:<a
    href="https://doi.org/10.1007/978-3-319-74772-9_7">10.1007/978-3-319-74772-9_7</a>'
  apa: 'Kazda, A., Kozik, M., McKenzie, R., &#38; Moore, M. (2018). Absorption and
    directed Jónsson terms. In J. Czelakowski (Ed.), <i>Don Pigozzi on Abstract Algebraic
    Logic, Universal Algebra, and Computer Science</i> (Vol. 16, pp. 203–220). Cham:
    Springer Nature. <a href="https://doi.org/10.1007/978-3-319-74772-9_7">https://doi.org/10.1007/978-3-319-74772-9_7</a>'
  chicago: 'Kazda, Alexandr, Marcin Kozik, Ralph McKenzie, and Matthew Moore. “Absorption
    and Directed Jónsson Terms.” In <i>Don Pigozzi on Abstract Algebraic Logic, Universal
    Algebra, and Computer Science</i>, edited by J Czelakowski, 16:203–20. OCTR. Cham:
    Springer Nature, 2018. <a href="https://doi.org/10.1007/978-3-319-74772-9_7">https://doi.org/10.1007/978-3-319-74772-9_7</a>.'
  ieee: 'A. Kazda, M. Kozik, R. McKenzie, and M. Moore, “Absorption and directed Jónsson
    terms,” in <i>Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and
    Computer Science</i>, vol. 16, J. Czelakowski, Ed. Cham: Springer Nature, 2018,
    pp. 203–220.'
  ista: 'Kazda A, Kozik M, McKenzie R, Moore M. 2018.Absorption and directed Jónsson
    terms. In: Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer
    Science. vol. 16, 203–220.'
  mla: Kazda, Alexandr, et al. “Absorption and Directed Jónsson Terms.” <i>Don Pigozzi
    on Abstract Algebraic Logic, Universal Algebra, and Computer Science</i>, edited
    by J Czelakowski, vol. 16, Springer Nature, 2018, pp. 203–20, doi:<a href="https://doi.org/10.1007/978-3-319-74772-9_7">10.1007/978-3-319-74772-9_7</a>.
  short: A. Kazda, M. Kozik, R. McKenzie, M. Moore, in:, J. Czelakowski (Ed.), Don
    Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science,
    Springer Nature, Cham, 2018, pp. 203–220.
date_created: 2022-03-18T10:30:32Z
date_published: 2018-03-21T00:00:00Z
date_updated: 2023-09-05T15:37:18Z
day: '21'
department:
- _id: VlKo
doi: 10.1007/978-3-319-74772-9_7
editor:
- first_name: J
  full_name: Czelakowski, J
  last_name: Czelakowski
external_id:
  arxiv:
  - '1502.01072'
intvolume: '        16'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1502.01072
month: '03'
oa: 1
oa_version: Preprint
page: 203-220
place: Cham
publication: Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer
  Science
publication_identifier:
  eisbn:
  - '9783319747729'
  eissn:
  - 2211-2766
  isbn:
  - '9783319747712'
  issn:
  - 2211-2758
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: OCTR
status: public
title: Absorption and directed Jónsson terms
type: book_chapter
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 16
year: '2018'
...