{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:40:18Z","timestamp":1760143218846,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T00:00:00Z","timestamp":1706140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Slovenian Research and Innovation Agency","award":["P2-0103"],"award-info":[{"award-number":["P2-0103"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we provide the basic properties of (semi)simple hypermodules. We show that if a hypermodule M is simple, then (End(M),\u00b7) is a group, where End(M) is the set of all normal endomorphisms of M. We prove that every simple hypermodule is normal projective with a zero singular subhypermodule. We also show that the class of semisimple hypermodules is closed under internal direct sums, factor hypermodules, and subhypermodules. In particular, we give a characterization of internal direct sums of subhypermodules of a hypermodule.<\/jats:p>","DOI":"10.3390\/axioms13020081","type":"journal-article","created":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T10:32:38Z","timestamp":1706178758000},"page":"81","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Hyperstructural Approach to Semisimplicity"],"prefix":"10.3390","volume":"13","author":[{"given":"Erg\u00fcl","family":"T\u00fcrkmen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Art and Science, Amasya University, 05100 Ipekkoy, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7900-0529","authenticated-orcid":false,"given":"Burcu","family":"N\u0130\u015fanc\u0131 T\u00fcrkmen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Art and Science, Amasya University, 05100 Ipekkoy, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3871-217X","authenticated-orcid":false,"given":"Hashem","family":"Bordbar","sequence":"additional","affiliation":[{"name":"Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,25]]},"reference":[{"unstructured":"Marty, F. 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