{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:15:36Z","timestamp":1760148936106,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T00:00:00Z","timestamp":1687132800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University","doi-asserted-by":"publisher","award":["PNURSP2023R231"],"award-info":[{"award-number":["PNURSP2023R231"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Group actions are a valuable tool for investigating the symmetry and automorphism features of rings. The concept of fuzzy ideals in rings has been expanded with the introduction of fuzzy primary, weak primary, and semiprimary ideals. This paper explores the existence of fuzzy ideals that are semiprimary but neither weak primary nor primary. Furthermore, it defines a group action on a fuzzy ideal and examines the properties of fuzzy ideals and their level cuts under this group action. In fact, it aims to investigate the relationship between fuzzy semiprimary ideals and the radical of fuzzy ideals under group action. Additionally, it includes the results related to the radical of fuzzy ideals and fuzzy G-semiprimary ideals. Moreover, the preservation of the image and inverse image of a fuzzy G-semiprimary ideal of a ring R under certain conditions is also studied. It delves into the algebraic nature of fuzzy ideals and the radical under G-homomorphism of fuzzy ideals.<\/jats:p>","DOI":"10.3390\/axioms12060606","type":"journal-article","created":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T02:26:56Z","timestamp":1687228016000},"page":"606","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Applications of Fuzzy Semiprimary Ideals under Group Action"],"prefix":"10.3390","volume":"12","author":[{"given":"Asma","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7856-2861","authenticated-orcid":false,"given":"Amal","family":"Alali","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"given":"Arshad","family":"Zishan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy Sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1016\/0022-247X(71)90199-5","article-title":"Fuzzy Groups","volume":"35","author":"Rosenfeld","year":"1971","journal-title":"J. Math. Anal. 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Intell. Fuzzy Syst."},{"key":"ref_11","first-page":"7821678","article-title":"Radical Structures of Fuzzy Polynomial Ideals in a Ring","volume":"2016","author":"Sik","year":"2016","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1007\/s13370-019-00670-7","article-title":"On almost fuzzy prime ideals and sub-modules","volume":"30","author":"Malik","year":"2019","journal-title":"Afr. Mat."},{"key":"ref_13","first-page":"74","article-title":"Fuzzy ideals in Laskerian rings","volume":"65","author":"Tariq","year":"2012","journal-title":"Mat. Vesn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"617","DOI":"10.46793\/KgJMat2204.617Y","article-title":"On fuzzy primary and fuzzy quasi-primary ideals in LA-semigroups","volume":"46","author":"Yiarayong","year":"2022","journal-title":"Kragujev. J. Math"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/6\/606\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:56:16Z","timestamp":1760126176000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/6\/606"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,19]]},"references-count":14,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["axioms12060606"],"URL":"https:\/\/doi.org\/10.3390\/axioms12060606","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2023,6,19]]}}}