MTL-代数中的稳定子
Stabilizers in MTL-algebras
摘要：
本文在MTL-代数中引入了一些稳定子并研究了它们的相关性质，然后利用这些稳定子刻画了一些特殊的MTL-代数，如IMTL-代数、积分MTL-代数、Gödel代数和MV-代数。此外，我们还讨论了MTL-代数中稳定子与几种特殊滤子（理想）之间的关系。最后，讨论了这两种稳定器之间的关系，证明了右关联稳定器与右乘稳定器是序同构的。这些结果也回答了Motamed和Torkzadeh在[Soft Comput，{ \bf 21}（2017）686-693]中提出的一些开放问题。
英文摘要：
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, {\bf 21} (2017) 686-693].
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