{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:49:24Z","timestamp":1747190964326,"version":"3.40.5"},"reference-count":32,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,6,26]],"date-time":"2022-06-26T00:00:00Z","timestamp":1656201600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2022,6,26]]},"abstract":"<jats:p>The concept of state has been considered in commutative and noncommutative logical systems, and their properties are at the center for the development of an algebraic investigation of probabilistic models for those algebras. This article mainly focuses on the study of the lattice of state ideals in De Morgan state residuated lattices (DMSRLs). First, we prove that the lattice of all state ideals <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                        <a:mi mathvariant=\"script\">S<\/a:mi>\n                        <a:mi mathvariant=\"normal\">\u2110<\/a:mi>\n                        <a:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <a:mrow>\n                              <a:mi>L<\/a:mi>\n                           <\/a:mrow>\n                        <\/a:mfenced>\n                     <\/a:math>\n                  <\/jats:inline-formula> of a DMSRL <jats:inline-formula>\n                     <h:math xmlns:h=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <h:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <h:mrow>\n                              <h:mi>L<\/h:mi>\n                              <h:mo>,<\/h:mo>\n                              <h:mi>\u03c4<\/h:mi>\n                           <\/h:mrow>\n                        <\/h:mfenced>\n                     <\/h:math>\n                  <\/jats:inline-formula> is a coherent frame. Then, we characterize the DMSRL for which the lattice <jats:inline-formula>\n                     <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <m:mi mathvariant=\"script\">S<\/m:mi>\n                        <m:mi mathvariant=\"normal\">\u2110<\/m:mi>\n                        <m:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <m:mrow>\n                              <m:mi>L<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:mfenced>\n                     <\/m:math>\n                  <\/jats:inline-formula> is a Boolean algebra. In addition, we bring in the concept of state relative annihilator of a given nonempty subset with respect to a state ideal in DMSRL and investigate various properties. We prove that state relative annihilators are a particular kind of state ideals. Finally, we investigate the notion of prime state ideal in DMSRL and establish the prime state ideal theorem.<\/jats:p>","DOI":"10.1155\/2022\/6213448","type":"journal-article","created":{"date-parts":[[2022,6,26]],"date-time":"2022-06-26T22:50:15Z","timestamp":1656283815000},"page":"1-14","source":"Crossref","is-referenced-by-count":0,"title":["On State Ideals and State Relative Annihilators in De Morgan State Residuated Lattices"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0479-4309","authenticated-orcid":true,"given":"Francis","family":"Woumfo","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9035-6753","authenticated-orcid":true,"given":"Blaise Bleriot","family":"Koguep Njionou","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6338-090X","authenticated-orcid":true,"given":"Etienne Romuald","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0784-1377","authenticated-orcid":true,"given":"Celestin","family":"Lele","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. 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