{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T04:29:23Z","timestamp":1761884963511,"version":"build-2065373602"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"name":"ERC","award":["101097307"],"award-info":[{"award-number":["101097307"]}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"crossref","award":["EP\/Y008626\/1"],"award-info":[{"award-number":["EP\/Y008626\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>We improve on earlier results on the closure under free products of the class of automaton semigroups. We consider partial automata and show that the free product of two self-similar semigroups (or automaton semigroups) is self-similar (an automaton semigroup) if there is a homomorphism from one of the base semigroups to the other. The construction used is computable and yields further consequences. One of them is that we can adjoin a free generator to any self-similar semigroup (or automaton semigroup) and preserve the property of self-similarity (or being an automaton semigroup). The existence of a homomorphism between two semigroups is a very lax requirement; in particular, it is satisfied if one of the semigroups contains an idempotent. To explore the limits of this requirement, we show that no simple or 0-simple idempotent-free semigroup is a finitely generated self-similar semigroup (or an automaton semigroup). Furthermore, we give an example of a pair of residually finite semigroups without a homomorphism from one to the other.<\/jats:p>","DOI":"10.1142\/s0218196725500353","type":"journal-article","created":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T06:25:02Z","timestamp":1753424702000},"page":"1091-1121","source":"Crossref","is-referenced-by-count":0,"title":["Preserving self-similarity in free products of semigroups"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3576-0670","authenticated-orcid":false,"given":"Tara Macalister","family":"Brough","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es, Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa, 2829\u2013516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7801-6569","authenticated-orcid":false,"given":"Jan Philipp","family":"W\u00e4chter","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-3973-5930","authenticated-orcid":false,"given":"Janette","family":"Welker","sequence":"additional","affiliation":[{"name":"Theoretical Computer Science Group, Goethe University Frankfurt, Robert-Mayer-Str. 11-15, 60325 Frankfurt am Main, Germany"}]}],"member":"219","published-online":{"date-parts":[[2025,9,4]]},"reference":[{"key":"S0218196725500353BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-014-9632-x"},{"key":"S0218196725500353BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2017.02.003"},{"key":"S0218196725500353BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2009.07.054"},{"key":"S0218196725500353BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2017.05.008"},{"key":"S0218196725500353BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-020-1972-5"},{"key":"S0218196725500353BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-020-10114-5"},{"key":"S0218196725500353BIB008","series-title":"Leibniz International Proceedings in Informatics (LIPIcs)","first-page":"44:1","volume-title":"49th Int. Symp. Mathematical Foundations of Computer Science (MFCS 2024)","volume":"306","author":"D\u2019Angeli D.","year":"2024"},{"key":"S0218196725500353BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196714500015"},{"key":"S0218196725500353BIB010","doi-asserted-by":"publisher","DOI":"10.1023\/A:1012061801279"},{"key":"S0218196725500353BIB011","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198511946.001.0001"},{"key":"S0218196725500353BIB012","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500018163"},{"key":"S0218196725500353BIB013","doi-asserted-by":"publisher","DOI":"10.12958\/adm2371"},{"key":"S0218196725500353BIB014","doi-asserted-by":"publisher","DOI":"10.30970\/ms.61.1.3-9"},{"key":"S0218196725500353BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(74)90146-X"},{"volume-title":"Finite Automata","year":"2004","author":"Lawson M. V.","key":"S0218196725500353BIB016"},{"key":"S0218196725500353BIB017","volume-title":"An Introduction to Formal Languages and Automata","author":"Linz P.","year":"2011","edition":"5"},{"key":"S0218196725500353BIB018","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196710005960"},{"key":"S0218196725500353BIB019","first-page":"11","volume-title":"Logic, Algebraic system, Language and Related Areas in Computer Science","volume":"2229","author":"Rodaro E.","year":"2022"},{"key":"S0218196725500353BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2011.02.049"},{"key":"S0218196725500353BIB021","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196705002761"},{"key":"S0218196725500353BIB022","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196711006194"},{"key":"S0218196725500353BIB023","doi-asserted-by":"publisher","DOI":"10.4171\/ggd\/87"},{"key":"S0218196725500353BIB025","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-021-10064-7"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196725500353","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T03:10:47Z","timestamp":1761880247000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196725500353"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,4]]},"references-count":23,"journal-issue":{"issue":"08","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["10.1142\/S0218196725500353"],"URL":"https:\/\/doi.org\/10.1142\/s0218196725500353","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2025,9,4]]}}}