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Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework\u2014pointed left-residuated <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ell $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u2113<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-groupoids\u2014where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ell $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u2113<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some parts of the theory of join-completions of residuated <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ell $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u2113<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-groupoids to the left-residuated case, giving a new proof of MacLaren\u2019s theorem for orthomodular lattices.<\/jats:p>","DOI":"10.1007\/s11225-021-09946-1","type":"journal-article","created":{"date-parts":[[2021,4,17]],"date-time":"2021-04-17T11:02:21Z","timestamp":1618657341000},"page":"1201-1239","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Residuated Structures and Orthomodular Lattices"],"prefix":"10.1007","volume":"109","author":[{"given":"D.","family":"Fazio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Ledda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"Paoli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,4,17]]},"reference":[{"key":"9946_CR1","volume-title":"Entailment","author":"AR Anderson","year":"1975","unstructured":"Anderson, A.R., and N.D. 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