{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T21:27:28Z","timestamp":1767907648059,"version":"3.49.0"},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12171213"],"award-info":[{"award-number":["12171213"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11771191"],"award-info":[{"award-number":["11771191"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004775","name":"Natural Science Foundation of Gansu Province","doi-asserted-by":"crossref","award":["20JR5RA275"],"award-info":[{"award-number":["20JR5RA275"]}],"id":[{"id":"10.13039\/501100004775","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:p> It is known, since the early 2000s, that the Catalan monoid [Formula: see text] generated by [Formula: see text] elements is finitely based if and only if [Formula: see text]. The main goal of this paper is to prove that the involution monoid [Formula: see text] is non-finitely based. Therefore, in contrast, combining with previous results yields that the involution Catalan monoid [Formula: see text] is finitely based if and only if [Formula: see text]. <\/jats:p><jats:p> The Kiselman monoid [Formula: see text] generated by [Formula: see text] elements is also considered. Although the semigroups [Formula: see text] and [Formula: see text] have recently been shown to satisfy the same identities, it is unknown if the same result holds when they are considered as involution semigroups. Nevertheless, it is deduced from the main result that the involution Kiselman monoid [Formula: see text] is finitely based if and only if [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196722500497","type":"journal-article","created":{"date-parts":[[2022,5,12]],"date-time":"2022-05-12T16:24:10Z","timestamp":1652372650000},"page":"1161-1177","source":"Crossref","is-referenced-by-count":4,"title":["Finite basis problem for Catalan monoids with involution"],"prefix":"10.1142","volume":"32","author":[{"given":"Meng","family":"Gao","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China"},{"name":"Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg 620000, Russia"}]},{"given":"Wen Ting","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. 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