{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:21:01Z","timestamp":1740122461619,"version":"3.37.3"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,2,28]],"date-time":"2023-02-28T00:00:00Z","timestamp":1677542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,2,28]],"date-time":"2023-02-28T00:00:00Z","timestamp":1677542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Categor Struct"],"published-print":{"date-parts":[[2023,4]]},"DOI":"10.1007\/s10485-023-09710-7","type":"journal-article","created":{"date-parts":[[2023,3,2]],"date-time":"2023-03-02T11:53:07Z","timestamp":1677757987000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some Modifications of Hull Operators in Archimedean Lattice-Ordered Groups with Weak Unit"],"prefix":"10.1007","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1355-0541","authenticated-orcid":false,"given":"Ricardo E.","family":"Carrera","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anthony W.","family":"Hager","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,2,28]]},"reference":[{"key":"9710_CR1","doi-asserted-by":"crossref","unstructured":"Anderson, M., Feil, T.: Lattice-Ordered Groups; An Introduction, Reidel Texts, Mathematical Sciences; Kluwer, Dordrecht (1988)","DOI":"10.1007\/978-94-009-2871-8"},{"issue":"1","key":"9710_CR2","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1216\/RMJ-1982-12-1-7","volume":"12","author":"M Anderson","year":"1982","unstructured":"Anderson, M., Conrad, P.F.: The Hulls of $$C(Y)$$. Rocky Mt. J. Math. 12(1), 7\u201322 (1982)","journal-title":"Rocky Mt. J. Math."},{"key":"9710_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0166-8641(81)90024-9","volume":"12","author":"ER Aron","year":"1981","unstructured":"Aron, E.R., Hager, A.W.: Convex vector lattices and $$\\ell $$-algebras. Topol. Appl. 12, 1\u201310 (1981)","journal-title":"Topol. Appl."},{"key":"9710_CR4","unstructured":"Balbes, R., Dwinger, P.: Distributive Lattices. University of Missouri Press (1974)"},{"key":"9710_CR5","doi-asserted-by":"crossref","unstructured":"Ball, R. N., Hager, A. W.: Characterization of epimorphisms in archimedean lattice-ordered group and vector lattices. In: Glass, A., Holland, W.C. (eds) Ch. 8 of Lattice-Ordered Groups, Advances and Techniques, Kluwer, (1989)","DOI":"10.1007\/978-94-009-2283-9_9"},{"key":"9710_CR6","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1017\/S1446788700035175","volume":"48","author":"RN Ball","year":"1990","unstructured":"Ball, R.N., Hager, A.W.: Epicompletion of archimedean $$\\ell $$-groups and vector lattices with weak unit. J. Aust. Math. Soc. 48, 25\u201356 (1990)","journal-title":"J. Aust. Math. Soc."},{"key":"9710_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0022-4049(93)90167-R","volume":"85","author":"RN Ball","year":"1993","unstructured":"Ball, R.N., Hager, A.W.: Algebraic extensions of an archimedean lattice-ordered group, I. J. Pure Appl. Algebr. 85, 1\u201320 (1993)","journal-title":"J. Pure Appl. Algebr."},{"key":"9710_CR8","doi-asserted-by":"crossref","unstructured":"Bigard, A., Keimel, K., Wolfenstein, S.: Groupes et Anneaux Reticules, Lecture Notes in Math. vol. 608, Springer , Berlin-Heidelberg-New York (1977)","DOI":"10.1007\/BFb0067004"},{"key":"9710_CR9","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1017\/S0004972700047286","volume":"5","author":"RD Bleier","year":"1971","unstructured":"Bleier, R.D.: Minimal vector lattice covers. Bull. Aust. Math. Soc. 5, 331\u2013335 (1971)","journal-title":"Bull. Aust. Math. Soc."},{"key":"9710_CR10","unstructured":"Carrera, R. E.: Operators on the Category of Archimedean Lattice-ordered Groups with Designated Weak Unit, Doctoral Dissertation, University of Florida, Gainesville, (2004)"},{"issue":"3","key":"9710_CR11","doi-asserted-by":"publisher","first-page":"411","DOI":"10.2478\/s12175-011-0020-7","volume":"61","author":"RE Carrera","year":"2011","unstructured":"Carrera, R.E., Hager, A.W.: On hull classes of $$\\ell $$-groups and covering classes of spaces. Math. Slovaca 61(3), 411\u2013428 (2011)","journal-title":"Math. Slovaca"},{"issue":"5","key":"9710_CR12","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1007\/s10485-014-9376-5","volume":"23","author":"RE Carrera","year":"2015","unstructured":"Carrera, R.E., Hager, A.W.: $$B$$-saturated hull classes in $$\\ell $$-groups and covering classes of spaces. Appl. Categ. Struct. 23(5), 709\u2013723 (2015)","journal-title":"Appl. Categ. Struct."},{"issue":"2","key":"9710_CR13","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/s10485-015-9391-1","volume":"24","author":"RE Carrera","year":"2016","unstructured":"Carrera, R.E., Hager, A.W.: Bounded equivalence of hull classes in archimedean lattice-ordered groups with unit. Appl. Categ. Struct. 24(2), 163\u2013179 (2016)","journal-title":"Appl. Categ. Struct."},{"issue":"1","key":"9710_CR14","first-page":"83","volume":"13","author":"RE Carrera","year":"2020","unstructured":"Carrera, R.E., Hager, A.W.: A classification of hull operators in archimedean lattice-ordered groups with unit. Categ. Gen. Algbr. Struct. Appl. 13(1), 83\u2013103 (2020)","journal-title":"Categ. Gen. Algbr. Struct. Appl."},{"key":"9710_CR15","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1215\/S0012-7094-71-03819-1","volume":"38","author":"PF Conrad","year":"1971","unstructured":"Conrad, P.F.: The essential closure of an archimedean lattice-ordered group. Duke Math. J. 38, 151\u2013160 (1971)","journal-title":"Duke Math. J."},{"key":"9710_CR16","unstructured":"Fine, N., Gillman, L., Lambek, J.: Rings of Quotients of Rings of Functions. McGill University Press (1965)"},{"key":"9710_CR17","unstructured":"Gillman, L., Jerison, M.: Rings of Continuous Functions, Grad. Texts in Math. vol. 43. Springer-Verlag, Berlin-Heidelberg-New York (1976)"},{"key":"9710_CR18","first-page":"482","volume":"2","author":"AM Gleason","year":"1958","unstructured":"Gleason, A.M.: Projective topological spaces. Ill. J. Math. 2, 482\u2013489 (1958)","journal-title":"Ill. J. Math."},{"key":"9710_CR19","unstructured":"Hager, A. W., Martinez, J.: $$\\alpha $$-projectable and laterally $$\\alpha $$-complete archimedean lattice-ordered groups, In: Proc. Conf. in Memory of T. Retta; S. Bernahu, ed.; Temple U. (1985); Ethiopian J. Sci., pp. 73-84 (1996)"},{"key":"9710_CR20","doi-asserted-by":"crossref","unstructured":"Hager, A.W.: Algebraic closures of $$\\ell $$-groups of continuous functions. In: Aull, C.E. (ed.) Dekker Notes Rings of Continuous Functions, vol. 95, pp. 165\u2013194 (1985)","DOI":"10.1201\/9781003072652-11"},{"issue":"19","key":"9710_CR21","doi-asserted-by":"publisher","first-page":"75","DOI":"10.5802\/afst.1276","volume":"6","author":"AW Hager","year":"2010","unstructured":"Hager, A.W., Johnson, D.G.: Some comments and examples on generations of (Hyper-)archimedean $$\\ell $$-groups and $$f$$-rings. Ann. Fac. Sci. Toulous Math 6(19), 75\u2013100 (2010)","journal-title":"Ann. Fac. Sci. Toulous Math"},{"issue":"5","key":"9710_CR22","doi-asserted-by":"publisher","first-page":"605","DOI":"10.1007\/s10485-016-9449-8","volume":"24","author":"AW Hager","year":"2016","unstructured":"Hager, A.W., Madden, J.J.: The $$H$$-closed monoreflections, implicit operations, and countable composition, in archimedean lattice-ordered groups with unit. Appl. Categ. Struct. 24(5), 605\u2013617 (2016)","journal-title":"Appl. Categ. Struct."},{"key":"9710_CR23","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1023\/A:1006323031986","volume":"16","author":"AW Hager","year":"1999","unstructured":"Hager, A.W., Martinez, J.: Hulls for various kinds of $$\\alpha $$-completeness in archimedean lattice-ordered groups. Order 16, 89\u2013103 (1999)","journal-title":"Order"},{"key":"9710_CR24","first-page":"87","volume":"105","author":"AW Hager","year":"2001","unstructured":"Hager, A.W., Martinez, J.: Functorial approximation to the lateral completion in archimedean lattice-ordered groups with weak unit. Rend. Semin. Mat. Univ. Padova 105, 87\u2013110 (2001)","journal-title":"Rend. Semin. Mat. Univ. Padova"},{"key":"9710_CR25","first-page":"411","volume":"21","author":"AW Hager","year":"1977","unstructured":"Hager, A.W., Robertson, L.C.: Representing and ringifying a Riesz space. Symp. Math. 21, 411\u2013431 (1977)","journal-title":"Symp. Math."},{"key":"9710_CR26","first-page":"97","volume":"59","author":"AW Hager","year":"1978","unstructured":"Hager, A.W., Robertson, L.C.: Extremal units in an archimedean Riesz space. Rend. Semin. Mat. Univ. Padova 59, 97\u2013115 (1978)","journal-title":"Rend. Semin. Mat. Univ. Padova"},{"key":"9710_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4153\/CJM-1979-001-5","volume":"31","author":"AW Hager","year":"1979","unstructured":"Hager, A.W., Robertson, L.C.: On the embedding into a ring of an archimedean $$\\ell $$-group. Can. J. Math. 31, 1\u20138 (1979)","journal-title":"Can. J. Math."},{"issue":"52","key":"9710_CR28","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1007\/BF02872765","volume":"2","author":"AW Hager","year":"2003","unstructured":"Hager, A.W., Kimber, C.M., McGovern, W.W.: Weakly least integer closed groups. Rend. Circ. Mat. Palermo 2(52), 453\u2013480 (2003)","journal-title":"Rend. Circ. Mat. Palermo"},{"key":"9710_CR29","doi-asserted-by":"publisher","first-page":"73","DOI":"10.4064\/fm-50-1-73-94","volume":"50","author":"M Henriksen","year":"1961","unstructured":"Henriksen, M., Johnson, D.G.: On the structure of a class of archimedean lattice-ordered algebras. Fundam. Math. 50, 73\u201394 (1961)","journal-title":"Fundam. Math."},{"key":"9710_CR30","unstructured":"Herrlich, H., Strecker, G.: Category Theory, Sigma Series in Pure Math, vol. 1, Heldermann Verlag, Berlin (1979)"},{"key":"9710_CR31","volume-title":"Riesz Spaces","author":"W Luxemburg","year":"1971","unstructured":"Luxemburg, W., Zaanen, A.: Riesz Spaces, vol. 1. North Holland, Amsterdam (1971)"},{"key":"9710_CR32","doi-asserted-by":"crossref","unstructured":"Martinez, J.: Hull classes of archimedean lattice-ordered groups with unit: A survey. In: Martinez, J. (ed.) Ordered Algebraic Structures: Proc. Gainesville Conf., 2001. Kluwer Acad. Pub., pp. 89-121 (2002)","DOI":"10.1007\/978-1-4757-3627-4_5"},{"key":"9710_CR33","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/j.jpaa.2003.10.029","volume":"190","author":"J Martinez","year":"2004","unstructured":"Martinez, J.: Polar Functions, II: completion classes of archimedean $$f$$-algebras vs. covers of compact spaces. J. Pure Appl. Algebr. 190, 225\u2013249 (2004)","journal-title":"J. Pure Appl. Algebr."}],"container-title":["Applied Categorical Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-023-09710-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10485-023-09710-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-023-09710-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T04:13:31Z","timestamp":1682482411000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10485-023-09710-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,28]]},"references-count":33,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["9710"],"URL":"https:\/\/doi.org\/10.1007\/s10485-023-09710-7","relation":{},"ISSN":["0927-2852","1572-9095"],"issn-type":[{"type":"print","value":"0927-2852"},{"type":"electronic","value":"1572-9095"}],"subject":[],"published":{"date-parts":[[2023,2,28]]},"assertion":[{"value":"24 May 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 January 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 February 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"12"}}