Affiliations: [a] School of Science, Xi’an Shiyou University, Xi’an, Shaanxi, China
| [b] School of Mathematics, Northwest University, Xi’an, P.R. China | [c] School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, P.R. China | [d] Mahani Mathematical research center, Shahid Bahonar University of Kerman, Kerman, Iran
| [e] Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Correspondence:
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Corresponding author. Peng Fei He, School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, P.R. China. E-mail: [email protected].
Abstract: In the paper, we introduce some stabilizers and investigate related properties of them in MTL-algebras. Then, we also characterize some special classes of MTL-algebras, for example, IMTL-algebras, integral MTL-algebras, Gödel algebras and MV-algebras, in terms of these stabilizers. Moreover, we discuss the relation between stabilizers and several special filters (ideals) in MTL-algebras. Finally, we discuss the relation between these stabilizers and prove that the right implicative stabilizer and right multiplicative stabilizer are order isomorphic. This results also give answers to some open problems, which were proposed by Motamed and Torkzadeh in [Soft Comput, 21 (2017) 686-693].
