{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,4]],"date-time":"2024-01-04T21:02:51Z","timestamp":1704402171509},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["New Math. and Nat. Computation"],"published-print":{"date-parts":[[2021,7]]},"abstract":"<jats:p> In random experiments, the fact that the sets of events has a structure of a Boolean algebra, i.e. it follows the rules of classical logic, is the main hypothesis of classical probability theory. Bosbach states have been introduced on commutative and non-commutative algebras of fuzzy logics as a way of probabilistically evaluating the formulas. In this paper, we focus on the relationship between some properties of ideals and Bosbach states in the framework of commutative residuated lattices. In particular, we introduce the concept of co-kernel of a Bosbach state which is an ideal and we establish the relationship between the notion of co-kernel and the kernel. Moreover, we define and characterize maximal ideals and maximal MV-ideals in residuated lattices. <\/jats:p>","DOI":"10.1142\/s1793005721500150","type":"journal-article","created":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T01:47:51Z","timestamp":1614649671000},"page":"281-302","source":"Crossref","is-referenced-by-count":1,"title":["Ideals and Bosbach States on Residuated Lattices"],"prefix":"10.1142","volume":"17","author":[{"given":"Francis","family":"Woumfo","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Dschang, P.O. Box 67, Dschang, Cameroon"}]},{"given":"Blaise B.","family":"Koguep Njionou","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Dschang, P.O. Box 67, Dschang, Cameroon"}]},{"given":"Etienne R.","family":"Temgoua Alomo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, \u00c9cole Normale Sup\u00e9rieure de Yaound\u00e9, University of Yaound\u00e9 1, P.O. Box 47, Yaound\u00e9, Cameroon"}]},{"given":"Celestin","family":"Lele","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Dschang, P.O. Box 67, Dschang, Cameroon"}]}],"member":"219","published-online":{"date-parts":[[2021,4,23]]},"reference":[{"key":"S1793005721500150BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2011.07.010"},{"key":"S1793005721500150BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s10773-013-1875-x"},{"key":"S1793005721500150BIB003","volume-title":"Algebras Foundations of Many-Valued Reasoning","author":"Cignoli R.","year":"2001"},{"key":"S1793005721500150BIB004","first-page":"175","volume":"2","author":"Ciungu L. 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