Stabilizers in MTL-algebras

TL;DR

This paper introduces stabilizers in MTL-algebras, characterizes special classes of these algebras using stabilizers, and explores their relations with filters and other stabilizers, addressing open problems in the field.

Contribution

It defines stabilizers in MTL-algebras, characterizes various algebra classes via stabilizers, and establishes isomorphisms between different stabilizers, solving existing open problems.

Findings

Stabilizers characterize classes like IMTL, G"odel, and MV-algebras.

Right implicative and right multiplicative stabilizers are order isomorphic.

The work answers open questions posed by Motamed and Torkzadeh.

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, G\"{o}del 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].