{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:55:30Z","timestamp":1760237730515,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,2]],"date-time":"2022-06-02T00:00:00Z","timestamp":1654128000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"DIPA LPPM Universitas Riau","award":["699\/UN.19.5.1.3\/PT.01.03\/2021"],"award-info":[{"award-number":["699\/UN.19.5.1.3\/PT.01.03\/2021"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A BN-algebra is a non-empty set X with a binary operation \u201c\u2217\u201d and a constant 0 that satisfies the following axioms: (B1)\u00a0x\u2217x=0,\u00a0(B2)\u00a0x\u22170=x, and (BN)\u00a0(x\u2217y)\u2217z=(0\u2217z)\u2217(y\u2217x) for all x,\u00a0y,\u00a0z\u00a0\u2208X. A non-empty subset I of X is called an ideal in BN-algebra X if it satisfies 0\u2208X and if y\u2208I and x\u2217y\u2208I, then x\u2208I for all x,y\u2208X. In this paper, we define several new ideal types in BN-algebras, namely, r-ideal, k-ideal, and m-k-ideal. Furthermore, some of their properties are constructed. Then, the relationships between ideals in BN-algebra with r-ideal, k-ideal, and m-k-ideal properties are investigated. Finally, the concept of r-ideal homomorphisms is discussed in BN-algebra.<\/jats:p>","DOI":"10.3390\/axioms11060268","type":"journal-article","created":{"date-parts":[[2022,6,2]],"date-time":"2022-06-02T11:05:02Z","timestamp":1654167902000},"page":"268","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On r-Ideals and m-k-Ideals in BN-Algebras"],"prefix":"10.3390","volume":"11","author":[{"given":"Sri","family":"Gemawati","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Sciences, University of Riau, Pekanbaru 28293, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Musnis","family":"Musraini","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Sciences, University of Riau, Pekanbaru 28293, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdul","family":"Hadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Sciences, University of Riau, Pekanbaru 28293, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5566-4264","authenticated-orcid":false,"given":"La","family":"Zakaria","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Sciences, Universitas Lampung, Bandar Lampung 35145, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elsi","family":"Fitria","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Sciences, University of Riau, Pekanbaru 28293, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,2]]},"reference":[{"key":"ref_1","first-page":"21","article-title":"On B-algebras","volume":"54","author":"Neggers","year":"2002","journal-title":"Mat. 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Appl."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/6\/268\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:23:47Z","timestamp":1760138627000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/6\/268"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,2]]},"references-count":11,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["axioms11060268"],"URL":"https:\/\/doi.org\/10.3390\/axioms11060268","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,6,2]]}}}