{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:44:35Z","timestamp":1740120275788,"version":"3.37.3"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100006753","name":"CMUP","doi-asserted-by":"crossref","award":["UID\/MAT\/00144\/2019"],"award-info":[{"award-number":["UID\/MAT\/00144\/2019"]}],"id":[{"id":"10.13039\/501100006753","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p> A regular semigroup is weakly generated by a set [Formula: see text] if it has no proper regular subsemigroup containing [Formula: see text]. In this paper, we study the regular semigroups weakly generated by idempotents. We show there exists a regular semigroup [Formula: see text] weakly generated by [Formula: see text] idempotents such that all other regular semigroups weakly generated by [Formula: see text] idempotents are homomorphic images of [Formula: see text]. The semigroup [Formula: see text] is defined by a presentation [Formula: see text] and its structure is studied. Although each of the sets [Formula: see text], [Formula: see text], and [Formula: see text] is infinite for [Formula: see text], we show that the word problem is decidable as each congruence class has a \u201ccanonical form\u201d. If [Formula: see text] denotes [Formula: see text] for [Formula: see text], we prove also that [Formula: see text] contains copies of all [Formula: see text] as subsemigroups. As a consequence, we conclude that (i) all regular semigroups weakly generated by a finite set of idempotents, which include all finitely idempotent generated regular semigroups, strongly divide [Formula: see text]; and (ii) all finite semigroups divide [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196723500388","type":"journal-article","created":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T05:51:51Z","timestamp":1685080311000},"page":"851-891","source":"Crossref","is-referenced-by-count":1,"title":["Regular semigroups weakly generated by idempotents"],"prefix":"10.1142","volume":"33","author":[{"given":"Lu\u00eds","family":"Oliveira","sequence":"first","affiliation":[{"name":"CMUP, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias da Universidade do Porto, R. 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