{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:28:29Z","timestamp":1747189709892,"version":"3.40.5"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"name":"the European Research Council","award":["101071674"],"award-info":[{"award-number":["101071674"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p> It is well known that an equivalence relation is invariant under the basic operations of an algebra if and only if it is invariant under the unary polynomials of the algebra. We show that a higher arity version of this property holds for a higher dimensional analogue of an equivalence relation. It follows that the [Formula: see text]-ary hypercommutator for an algebra is determined by its [Formula: see text]-ary polynomials. We construct examples to show that this fails for every arity of the term condition higher commutator. <\/jats:p>","DOI":"10.1142\/s0218196724500371","type":"journal-article","created":{"date-parts":[[2024,7,5]],"date-time":"2024-07-05T06:05:46Z","timestamp":1720159546000},"page":"919-936","source":"Crossref","is-referenced-by-count":0,"title":["Mal\u2019cev complexes"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7117-1400","authenticated-orcid":false,"given":"Andrew","family":"Moorhead","sequence":"first","affiliation":[{"name":"Institue f\u00fcr Algebra, Technische Universit\u00e4t Dresden Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,7,31]]},"reference":[{"key":"S0218196724500371BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-010-0084-1"},{"key":"S0218196724500371BIB002","first-page":"41","volume-title":"Contributions to General Algebra","volume":"13","author":"Bulatov A.","year":"2001"},{"key":"S0218196724500371BIB003","series-title":"London Mathematical Society Lecture Note Series","volume-title":"Commutator Theory for Congruence Modular Varieties","volume":"125","author":"Freese R.","year":"1987"},{"key":"S0218196724500371BIB004","doi-asserted-by":"publisher","DOI":"10.1090\/memo\/0286"},{"issue":"1","key":"S0218196724500371BIB005","first-page":"119","volume":"41","author":"Herrmann C.","year":"1979","journal-title":"Acta Sci. Math."},{"issue":"15","key":"S0218196724500371BIB006","first-page":"408","volume":"8","author":"Janelidze G.","year":"2001","journal-title":"Theory Appl. Categ."},{"issue":"1046","key":"S0218196724500371BIB007","first-page":"viii+169","volume":"222","author":"Kearnes K. A.","year":"2013","journal-title":"Mem. Amer. Math. Soc."},{"key":"S0218196724500371BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196798000247"},{"key":"S0218196724500371BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-022-00772-7"},{"key":"S0218196724500371BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/BF01195263"},{"key":"S0218196724500371BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2019.07.002"},{"key":"S0218196724500371BIB012","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/8251"},{"key":"S0218196724500371BIB013","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196722500539"},{"key":"S0218196724500371BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/BF01195141"},{"key":"S0218196724500371BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0095447"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196724500371","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,27]],"date-time":"2024-09-27T07:45:40Z","timestamp":1727423140000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196724500371"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,31]]},"references-count":15,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["10.1142\/S0218196724500371"],"URL":"https:\/\/doi.org\/10.1142\/s0218196724500371","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2024,7,31]]}}}