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The semigroup $${{\\,\\textrm{F}\\,}}(X)$$<\/jats:tex-math>\n \n \n \n F<\/mml:mtext>\n \n <\/mml:mrow>\n (<\/mml:mo>\n X<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is introduced by a presentation and the word problem for that presentation is solved. The structure of the semigroup $${{\\,\\textrm{F}\\,}}(X)$$<\/jats:tex-math>\n \n \n \n F<\/mml:mtext>\n \n <\/mml:mrow>\n (<\/mml:mo>\n X<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is also studied.<\/jats:p>","DOI":"10.1007\/s00233-024-10475-1","type":"journal-article","created":{"date-parts":[[2024,10,7]],"date-time":"2024-10-07T16:01:44Z","timestamp":1728316904000},"page":"639-668","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Regular semigroups weakly generated by set"],"prefix":"10.1007","volume":"109","author":[{"given":"Lu\u00eds","family":"Oliveira","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,10,7]]},"reference":[{"key":"10475_CR1","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1006\/jabr.1994.1169","volume":"166","author":"K Auinger","year":"1994","unstructured":"Auinger, K.: The bifree locally inverse semigroup on a set. 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