{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T02:39:02Z","timestamp":1774406342570,"version":"3.50.1"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"name":"NSF","award":["DMS-1500254"],"award-info":[{"award-number":["DMS-1500254"]}]},{"name":"Austrian Science Fund","award":["P33878"],"award-info":[{"award-number":["P33878"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:p> Clonoids are sets of finitary functions from an algebra [Formula: see text] to an algebra [Formula: see text] that are closed under composition with term functions of [Formula: see text] on the domain side and with term functions of [Formula: see text] on the codomain side. For [Formula: see text] (polynomially equivalent to) finite modules we show: If [Formula: see text] have coprime order and the congruence lattice of [Formula: see text] is distributive, then there are only finitely many clonoids from [Formula: see text] to [Formula: see text]. This is proved by establishing for every natural number k a particular linear equation that all k-ary functions from [Formula: see text] to [Formula: see text] satisfy. Else if [Formula: see text] do not have coprime order, then there exist infinite ascending chains of clonoids from [Formula: see text] to [Formula: see text] ordered by inclusion. Consequently any extension of [Formula: see text] by [Formula: see text] has countably infinitely many 2-nilpotent expansions up to term equivalence. <\/jats:p>","DOI":"10.1142\/s021819672450022x","type":"journal-article","created":{"date-parts":[[2024,4,19]],"date-time":"2024-04-19T03:53:36Z","timestamp":1713498816000},"page":"543-570","source":"Crossref","is-referenced-by-count":5,"title":["Clonoids between modules"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1163-313X","authenticated-orcid":false,"given":"Peter","family":"Mayr","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Colorado, Boulder, CO 80309, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-8687-5823","authenticated-orcid":false,"given":"Patrick","family":"Wynne","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Colorado, Boulder, CO 80309, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,5,25]]},"reference":[{"key":"S021819672450022XBIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2016.01.001"},{"key":"S021819672450022XBIB002","doi-asserted-by":"publisher","DOI":"10.1145\/3457606"},{"key":"S021819672450022XBIB003","first-page":"1","volume-title":"Dagstuhl Follow-Ups","volume":"7","author":"Barto L.","year":"2017"},{"key":"S021819672450022XBIB004","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511542794"},{"key":"S021819672450022XBIB005","doi-asserted-by":"publisher","DOI":"10.7151\/dmgaa.1153"},{"key":"S021819672450022XBIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s11083-022-09596-5"},{"key":"S021819672450022XBIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-021-00748-z"},{"key":"S021819672450022XBIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196721500302"},{"key":"S021819672450022XBIB009","series-title":"London Mathematical Society Lecture Note Series","volume-title":"Commutator Theory for Congruence Modular Varieties","volume":"125","author":"Freese R.","year":"1987"},{"key":"S021819672450022XBIB010","series-title":"Mathematical Surveys and Monographs","volume-title":"Algebras, Lattices, Varieties","author":"Freese R. 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