{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:16:05Z","timestamp":1760058965109,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T00:00:00Z","timestamp":1747094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University Researchers Supporting Project","award":["PNURSP2025R183"],"award-info":[{"award-number":["PNURSP2025R183"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, we define and study graded 1-absorbing prime ideals and graded weakly 1-absorbing prime ideals in non-commutative graded rings as a new class of graded ideals that lies between graded prime ideals (graded weakly prime ideals) and graded 2-absorbing ideals (graded weakly 2-absorbing ideals). Let G be a group and let R be a non-commutative G-graded ring with nonzero unity. Let P be a proper graded ideal of R. We then say that P is a graded 1-absorbing prime ideal (a graded weakly 1-absorbing prime ideal) of R if, for each nonunit homogeneous element r,s,t\u2208R with rRsRt\u2286P ({0}\u2260rRsRt\u2286P), either rs\u2208P or t\u2208P. We present a number of properties and characterizations of these graded ideals.<\/jats:p>","DOI":"10.3390\/axioms14050365","type":"journal-article","created":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T06:40:23Z","timestamp":1747118423000},"page":"365","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Graded 1-Absorbing Prime Ideals over Non-Commutative Graded Rings"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2893-576X","authenticated-orcid":false,"given":"Azzh Saad","family":"Alshehry","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8998-7590","authenticated-orcid":false,"given":"Rashid","family":"Abu-Dawwas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yarmouk University, Irbid 21163, Jordan"}]},{"given":"Rahaf","family":"Abudalo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yarmouk University, Irbid 21163, Jordan"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Nastasescu, C., and Oystaeyen, F. (2004). Methods of Graded Rings, Springer. Lecture Notes in Mathematics.","DOI":"10.1007\/b94904"},{"key":"ref_2","first-page":"85","article-title":"Graded classical weakly prime submodules over non-commutative graded rings","volume":"87","author":"Habeb","year":"2024","journal-title":"Tatra Mt. Math. 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Symmetry, 14.","DOI":"10.3390\/sym14071472"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1007\/s40863-022-00348-2","article-title":"1-absorbing prime ideals and weakly 1-absorbing prime ideals in non-commutative rings","volume":"17","author":"Groenewald","year":"2022","journal-title":"Sao Paulo J. Math. Sci."},{"key":"ref_12","first-page":"601","article-title":"On graded 2-absorbing quasi primary ideals","volume":"43","author":"Uregen","year":"2019","journal-title":"Southeast Asian Bull. Math."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/365\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:31:46Z","timestamp":1760031106000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/365"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,13]]},"references-count":12,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["axioms14050365"],"URL":"https:\/\/doi.org\/10.3390\/axioms14050365","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,5,13]]}}}