On derivations of EQ-algebras

Article type: Research Article

Authors: Liang, Jie | Xin, Xiao Long^{; *} | Wang, Jun Tao

Affiliations: College of Mathematics, Northwest University, Xi’an, P.R. China

Correspondence: [*] Corresponding author. Xiao Long Xin, College of Mathematics, Northwest University, Xi’an, 710127, P.R. China. E-mail: xlxin@nwu.edu.cn.

Abstract: The main goal of this paper is to introduce the notions of derivations on EQ-algebras and obtain several special types of them. In this paper, we discuss some properties of useful derivations and give some characterisations of them. Then, we also show that the fixed point set of useful derivations is a good EQ-algebra. Moreover, we study simple ⊙-derivations and their adjoint derivations and prove that the fixed point set of simple ⊙-derivations and that of their adjoint derivations are order isomorphism. Furthermore, the quotient algebras induced by d-filter are studied.

Keywords: EQ-algebra, derivation, fixed point set, simple

DOI: 10.3233/JIFS-18958

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 5, pp. 5573-5583, 2018