{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:03:07Z","timestamp":1760241787669,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T00:00:00Z","timestamp":1534464000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The notions of neutrosophy, neutrosophic algebraic structures, neutrosophic duplet and neutrosophic triplet were introduced by Florentin Smarandache. In this paper, the neutrosophic duplets of     Z  p n     ,     Z  p q      and     Z   p 1   p 2  \u2026  p n       are studied. In the case of     Z  p n      and     Z  p q     , the complete characterization of neutrosophic duplets are given. In the case of     Z   p 1  \u2026  p n      , only the neutrosophic duplets associated with     p i    s are provided;     i = 1 , 2 , \u2026 , n    . Some open problems related to neutrosophic duplets are proposed.<\/jats:p>","DOI":"10.3390\/sym10080345","type":"journal-article","created":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T10:54:25Z","timestamp":1534503265000},"page":"345","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Neutrosophic Duplets of {Zpn,\u00d7} and {Zpq,\u00d7} and Their Properties"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9832-1475","authenticated-orcid":false,"given":"Vasantha","family":"Kandasamy W.B.","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, VIT, Vellore 632014, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4826-9466","authenticated-orcid":false,"given":"Ilanthenral","family":"Kandasamy","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, VIT, Vellore 632014, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5560-5926","authenticated-orcid":false,"given":"Florentin","family":"Smarandache","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301, USA"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,17]]},"reference":[{"key":"ref_1","unstructured":"Smarandache, F. 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Appl."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/8\/345\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:19:15Z","timestamp":1760195955000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/8\/345"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,17]]},"references-count":25,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2018,8]]}},"alternative-id":["sym10080345"],"URL":"https:\/\/doi.org\/10.3390\/sym10080345","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2018,8,17]]}}}