Yue Xi

Bio: Yue Xi is an academic researcher from Jiangnan University. The author has contributed to research in topics: Type (model theory) & Prime (order theory). The author has co-authored 2 publications.

A New Type Soft Prime Ideal of KU-algebras

Abstract: Through combining the soft set with KU-algebras, this paper introduces the concept of a new type soft prime ideal of KU-algebras and investigates its properties. Firstly, we give the equivalent descriptions of the new type prime soft ideal of KU-algebras. Then, we show the differences between the new type soft prime ideal of KU-algebras and the common soft prime ideal of KU-algebras by giving examples. After then, studies about the equivalent description of the new type soft prime ideal and the new type soft ideal prove that the algebraic structure of dual soft set is different from the algebraic structure of \(\alpha \)-level set. Besides, we define the new concept of the projection of AND operation of soft set, and the obtain that the projection of AND operation of two soft set is also the new type soft prime ideal, if the AND operation is a new type soft prime ideal of KU-algebras. Finally, we explore the properties of the new type soft prime ideal of KU-algebras about the image and inverse image.

On Derivations of FI-Algebras

Abstract: In this paper, firstly, the concept of a new type of derivations on FI-algebras is introduced. The existence of it is verified by an example and a program. Then, the concepts of different kinds of derivations on FI-algebras are given. The properties of derivations on FI-algebras and the relationship between derivations and ideal are investigated. The equivalent conditions of identity derivation and the equivalent conditions of isotone derivation are proved. Finally, the concept of \(a-\)principal derivations on DFI-algebras is given. The existence of \(a-\)principal derivations is verified by an example and a program.