{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:56:09Z","timestamp":1760144169599,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,3,27]],"date-time":"2024-03-27T00:00:00Z","timestamp":1711497600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union under the Horizon Europe","award":["101074004 (C2IMPRESS)","LA\/P\/0112\/2020","UIDP\/04044\/2020","UIDB\/04044\/2020","MR-220617"],"award-info":[{"award-number":["101074004 (C2IMPRESS)","LA\/P\/0112\/2020","UIDP\/04044\/2020","UIDB\/04044\/2020","MR-220617"]}]},{"name":"Associate Laboratory","award":["101074004 (C2IMPRESS)","LA\/P\/0112\/2020","UIDP\/04044\/2020","UIDB\/04044\/2020","MR-220617"],"award-info":[{"award-number":["101074004 (C2IMPRESS)","LA\/P\/0112\/2020","UIDP\/04044\/2020","UIDB\/04044\/2020","MR-220617"]}]},{"name":"Centre for Rapid and Sustainable Product Development","award":["101074004 (C2IMPRESS)","LA\/P\/0112\/2020","UIDP\/04044\/2020","UIDB\/04044\/2020","MR-220617"],"award-info":[{"award-number":["101074004 (C2IMPRESS)","LA\/P\/0112\/2020","UIDP\/04044\/2020","UIDB\/04044\/2020","MR-220617"]}]},{"name":"Predictability of Complex Coevolutionary Systems","award":["101074004 (C2IMPRESS)","LA\/P\/0112\/2020","UIDP\/04044\/2020","UIDB\/04044\/2020","MR-220617"],"award-info":[{"award-number":["101074004 (C2IMPRESS)","LA\/P\/0112\/2020","UIDP\/04044\/2020","UIDB\/04044\/2020","MR-220617"]}]},{"name":"Quantum Information Technologies in the Earth Sciences","award":["101074004 (C2IMPRESS)","LA\/P\/0112\/2020","UIDP\/04044\/2020","UIDB\/04044\/2020","MR-220617"],"award-info":[{"award-number":["101074004 (C2IMPRESS)","LA\/P\/0112\/2020","UIDP\/04044\/2020","UIDB\/04044\/2020","MR-220617"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>A generalized construction procedure for algebraic number systems is hereby presented. This procedure offers an efficient representation and computation method for complex numbers, quaternions, and other algebraic structures. The construction method is then illustrated across a range of examples. In particular, the novel developments reported herein provide a generalized form of the Cayley\u2013Dickson construction through involutive dimagmas, thereby allowing for the treatment of more general spaces other than vector spaces, which underlie the associated algebra structure.<\/jats:p>","DOI":"10.3390\/math12070996","type":"journal-article","created":{"date-parts":[[2024,3,27]],"date-time":"2024-03-27T14:17:34Z","timestamp":1711549054000},"page":"996","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Towards a Generalized Cayley\u2013Dickson Construction through Involutive Dimagmas"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4199-7367","authenticated-orcid":false,"given":"Nelson","family":"Martins-Ferreira","sequence":"first","affiliation":[{"name":"Centre for Rapid and Sustainable Product Development, School of Technology and Management, Polytechnic Institute of Leiria, 2411-901 Leiria, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5543-1754","authenticated-orcid":false,"given":"Rui A. P.","family":"Perdig\u00e3o","sequence":"additional","affiliation":[{"name":"IUC Physics of Complex Coevolutionary Systems and Fluid Dynamical Systems, Meteoceanics Institute for Complex System Science, Washington, DC 20004, USA"},{"name":"Synergistic Manifolds, 1600-207 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1080\/14786444508562684","article-title":"On certain results relating to quaternions","volume":"26","author":"Cayley","year":"1845","journal-title":"Lond. Edinb. Dublin Philos. Mag. J. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"155","DOI":"10.2307\/1967865","article-title":"On Quaternions and Their Generalization and the History of the Eight Square Theorem","volume":"20","author":"Dickson","year":"1919","journal-title":"Ann. 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