{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T08:32:23Z","timestamp":1777365143583,"version":"3.51.4"},"reference-count":19,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,5,4]],"date-time":"2021-05-04T00:00:00Z","timestamp":1620086400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["P1-0285"],"award-info":[{"award-number":["P1-0285"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Inspired by the concepts of projective and injective modules in classical algebraic structure theory, in this paper we initiate the study of the chains of hypermodules over a Krasner hyperring R, endowing first the set HomRn(M,N) of all normal homomorphisms between two R-hypermodules M and N with a structure of R-hypermodule. Then, our study focuses on the concepts of normal injectivity and projectivity of hypermodules over a Krasner hyperring R, characterizing them by the mean of chains of R-hypermodules.<\/jats:p>","DOI":"10.3390\/axioms10020083","type":"journal-article","created":{"date-parts":[[2021,5,5]],"date-time":"2021-05-05T11:06:01Z","timestamp":1620212761000},"page":"83","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["About the Normal Projectivity and Injectivity of Krasner Hypermodules"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3871-217X","authenticated-orcid":false,"given":"Hashem","family":"Bordbar","sequence":"first","affiliation":[{"name":"Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5182-4136","authenticated-orcid":false,"given":"Irina","family":"Cristea","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":[[2021,5,4]]},"reference":[{"key":"ref_1","unstructured":"Krasner, M. 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Projective and Injective Krasner Hypermodules. J. Algebra Appl.","DOI":"10.1142\/S0219498821501863"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Halmos, P.R. (1974). Lectures on Boolean Algebras, Springer.","DOI":"10.1007\/978-1-4612-9855-7"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/BF01898828","article-title":"Categorical characterization of the MacNeille Completion","volume":"18","author":"Banaschewski","year":"1967","journal-title":"Arch. Math."},{"key":"ref_19","first-page":"889","article-title":"Hyperanneaux non commutatifs: Hyperanneaux artiniens, centralisateur d\u2019un hypermodule et theoreme de densite","volume":"269","author":"Stratigopoulos","year":"1969","journal-title":"C. R. Acad. Sci. 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