Affiliations: [a]
College of Mathematics, Northwest University, Xi’an, P.R. China | [b]
School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, P.R. China | [c]
School of Cyber Engnieering, Xidian University, Xi’an, P.R. China
Correspondence:
[*]
Corresponding author. Xiaolong Xin, Department of Mathematics, Northwest University, Xi’an, 710127, P. R.
China. Tel: +86 13571952880. E-mail: [email protected].
Abstract: In this paper, we introduce and study states on hyper MV-algebras. First, we introduce the notions of Riečan states and Bosbach states on a hyper MV-algebra and derive some properties of them. Also, we investigate and characterize regular Riečan states and regular Bosbach states on a hyper MV-algebra. Moreover, using a Bosbach state on a hyper MV-algebra, we construct and discuss a quotient hyper MV-algebra. In particular, we obtain some equivalent conditions under which a quotient hyper MV-algebra becomes a Boolean algebra. Finally, we introduce the notion of state morphisms on hyper MV-algebras, and discuss some relationships between state morphisms and Bosbach states.
Keywords: Hyper MV-algebra, Riečan state, Bosbach state, state morphism
