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We also introduce the concept of quasi ideals and show that any ideal is a quasi ideal, but the converse does not hold in general. We clarify the relations between these ideals in residuated lattices, strong residuated lattices and BL-algebras. For instance, we prove that in strong residuated lattices the concept of quasi ideals and ideals are the same and in BL-algebras the concepts of quasi ideals, ideals, strong ideals and MV-ideals coincide, whereas they are different in residuated lattices and MTL-algebras. We detect the relation between these ideals with MV-algebras, strong algebras and Boolean algebras.<\/jats:p>","DOI":"10.3233\/jifs-171197","type":"journal-article","created":{"date-parts":[[2018,5,1]],"date-time":"2018-05-01T10:18:32Z","timestamp":1525169912000},"page":"5647-5655","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Some types of ideals in residuated lattices"],"prefix":"10.1177","volume":"35","author":[{"given":"S. Khosravi","family":"Shoar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Fasa University, Fasa, Iran"}]}],"member":"179","published-online":{"date-parts":[[2018,5]]},"reference":[{"key":"e_1_3_2_2_2","unstructured":"BalbesR. and DwingerPh. Distributive lattices. 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