{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T18:27:12Z","timestamp":1769711232879,"version":"3.49.0"},"reference-count":11,"publisher":"SAGE Publications","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2023,11,4]]},"abstract":"<jats:p>Algebras of Logic deal with some algebraic structures, often bounded lattices, considered as models of certain logics, including logic as a domain of order theory. There are well known their importance and applications in social life to advance useful concepts, as for example computer algebra. Starting from results obtained by Di Nolla and Lettieri in [1], in which they analyzed the structure of finite BL-algebras, in this paper we find properties and give examples of commutative unitary rings R with its set of ideals Id\u00a0(R) to be a BL-algebra of a given type. Moreover, we present properties of finite rings or rings with a finite number of ideals in their connections with BL-rings.<\/jats:p>","DOI":"10.3233\/jifs-232815","type":"journal-article","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T11:13:56Z","timestamp":1694776436000},"page":"8613-8622","source":"Crossref","is-referenced-by-count":0,"title":["Remarks regarding some Algebras of Logic"],"prefix":"10.1177","volume":"45","author":[{"given":"Mariana Floricica","family":"C\u0103lin","sequence":"first","affiliation":[{"name":"Faculty of Psychology and Educational Science, Ovidius University of Constan\u0163a, Rom\u00e2nia"}]},{"given":"Cristina","family":"Flaut","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Ovidius University, Constan\u0163a, Rom\u00e2nia"}]},{"given":"Dana","family":"Piciu","sequence":"additional","affiliation":[{"name":"Faculty of Science, University of Craiova, Craiova, Rom\u00e2nia"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-232815_ref1","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/S0012-365X(02)00754-9","article-title":"Finite BL-algebras","volume":"269","author":"Di Nola","year":"2003","journal-title":"Discrete Mathematics"},{"key":"10.3233\/JIFS-232815_ref3","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1090\/S0002-9947-1939-1501995-3","article-title":"Residuated lattices","volume":"45","author":"Ward","year":"1939","journal-title":"Trans Am Math Soc"},{"key":"10.3233\/JIFS-232815_ref4","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1007\/s00500-021-06545-z","article-title":"Rings and residuated lattices whose fuzzy ideals form a Boolean algebra","volume":"26","author":"Tchoffo Foka","year":"2022","journal-title":"Soft Computing"},{"key":"10.3233\/JIFS-232815_ref6","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1090\/S0002-9947-1958-0094302-9","article-title":"Algebraic analysis of many-valued logic","volume":"88","author":"Chang","year":"1958","journal-title":"Trans Amer Math Soc"},{"issue":"3","key":"10.3233\/JIFS-232815_ref9","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1093\/jigpal\/jzy001","article-title":"BL-rings","volume":"26","author":"Heubo-Kwegna","year":"2018","journal-title":"Logic Journal of the IGPL"},{"issue":"11","key":"10.3233\/JIFS-232815_ref10","doi-asserted-by":"crossref","first-page":"4533","DOI":"10.1080\/00927872.2018.1543428","article-title":"Characterization of multiplication commutative rings with finitely many minimal prime ideals","volume":"47","author":"Alsuraiheed","year":"2019","journal-title":"Communications in Algebra"},{"issue":"4","key":"10.3233\/JIFS-232815_ref11","doi-asserted-by":"crossref","first-page":"760","DOI":"10.4153\/CJM-1976-072-1","article-title":"Multiplication ideals, multiplication rings, and the ring R(X)","volume":"28","author":"Anderson","year":"1976","journal-title":"Can J Math"},{"key":"10.3233\/JIFS-232815_ref12","doi-asserted-by":"crossref","unstructured":"Anderson F.W. and Fuller K. , Rings and categories of modules, Graduate Texts in Mathematics 13 (1992), 2 ed., Springer-Verlag, New York.","DOI":"10.1007\/978-1-4612-4418-9"},{"key":"10.3233\/JIFS-232815_ref13","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s40065-012-0003-8","article-title":"A note on zero-divisors of commutative rings","volume":"1","author":"Filipowicz","year":"2012","journal-title":"Arab J Math"},{"issue":"6","key":"10.3233\/JIFS-232815_ref14","first-page":"93","article-title":"Connections between commutative rings and some algebras of logic","volume":"19","author":"Flaut","year":"2022","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"10.3233\/JIFS-232815_ref15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3390\/math10244739","article-title":"Some Examples of BL-Algebras Using Commutative Rings","volume":"10","author":"Flaut","year":"2022","journal-title":"Mathematics"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-232815","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T07:27:03Z","timestamp":1769671623000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-232815"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,4]]},"references-count":11,"journal-issue":{"issue":"5"},"URL":"https:\/\/doi.org\/10.3233\/jifs-232815","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,4]]}}}