{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:19Z","timestamp":1753894399249,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We study the variety ZG of monoids where the elements that belong to a group\nare central, i.e., commute with all other elements. We show that ZG is local,\nthat is, the semidirect product ZG * D of ZG by definite semigroups is equal to\nLZG, the variety of semigroups where all local monoids are in ZG. Our main\nresult is thus: ZG * D = LZG. We prove this result using Straubing's delay\ntheorem, by considering paths in the category of idempotents. In the process,\nwe obtain the characterization ZG = MNil \\vee Com, and also characterize the ZG\nlanguages, i.e., the languages whose syntactic monoid is in ZG: they are\nprecisely the languages that are finite unions of disjoint shuffles of\nsingleton languages and regular commutative languages.<\/jats:p>","DOI":"10.46298\/lmcs-19(4:4)2023","type":"journal-article","created":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T06:55:14Z","timestamp":1697612114000},"source":"Crossref","is-referenced-by-count":0,"title":["Locality and Centrality: The Variety ZG"],"prefix":"10.46298","volume":"Volume 19, Issue 4","author":[{"given":"Antoine","family":"Amarilli","sequence":"first","affiliation":[]},{"given":"Charles","family":"Paperman","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2023,10,18]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/lmcs.episciences.org\/12431\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/lmcs.episciences.org\/12431\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T06:55:28Z","timestamp":1697612128000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/11555"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,18]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-19(4:4)2023","relation":{"has-preprint":[{"id-type":"arxiv","id":"2102.07724v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2102.07724","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2102.07724","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2023,10,18]]},"article-number":"11555"}}