{"title":"Absorption and directed Jónsson terms","quality_controlled":"1","status":"public","publisher":"Springer Nature","scopus_import":"1","oa":1,"oa_version":"Preprint","series_title":"OCTR","date_created":"2022-03-18T10:30:32Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"VlKo"}],"abstract":[{"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.","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1502.01072","open_access":"1"}],"publication_status":"published","date_published":"2018-03-21T00:00:00Z","month":"03","article_processing_charge":"No","date_updated":"2023-09-05T15:37:18Z","type":"book_chapter","day":"21","acknowledgement":"The second author was supported by National Science Center grant DEC-2011-/01/B/ST6/01006.","year":"2018","intvolume":"        16","volume":16,"editor":[{"first_name":"J","last_name":"Czelakowski","full_name":"Czelakowski, J"}],"language":[{"iso":"eng"}],"_id":"10864","citation":{"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>.","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.","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>","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>.","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>","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.","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."},"external_id":{"arxiv":["1502.01072"]},"publication_identifier":{"issn":["2211-2758"],"isbn":["9783319747712"],"eissn":["2211-2766"],"eisbn":["9783319747729"]},"doi":"10.1007/978-3-319-74772-9_7","page":"203-220","place":"Cham","publication":"Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science","author":[{"last_name":"Kazda","first_name":"Alexandr","full_name":"Kazda, Alexandr","id":"3B32BAA8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Marcin","last_name":"Kozik","full_name":"Kozik, Marcin"},{"last_name":"McKenzie","first_name":"Ralph","full_name":"McKenzie, Ralph"},{"full_name":"Moore, Matthew","last_name":"Moore","first_name":"Matthew"}]}