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Some types of filters in MTL-algebras |
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| Authors: | RA Borzooei R Ameri |
| Institution: | a Department of Mathematics, Shahid Beheshti University, Tehran, Iran b Department of Mathematics, Payam Noor University, Tehran, Iran c Department of Mathematics, Tehran University, Tehran, Iran |
| Abstract: | The aim of this work is to introduce the concepts of IMTL-filters and strong MTL-filters in MTL-algebras and show that these filters are related to IMTL-algebras and strong MTL-algebras, respectively. We also introduce the concepts of EIMTL and associative filters in MTL-algebras. The relationships between these filters and quotient algebras that are constructed via these filters are described. We clarify that EIMTL, IMTL and fantastic filters coincide in BL-algebras, whereas they have different properties in MTL-algebras; moreover, the relations between them are delineated. We prove that strong filters include some current filters such as implicative, positive implicative and fantastic filters. |
| Keywords: | MTL-algebra BL-algebra EIMTL-filter IMTL-filter Strong filter Fantastic filter (positive) Implicative filter |
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