State hyper BE-algebras

Document Type : Original Article


1 School of Science, Xi'an Aeronautical University, Xi'an, 710077, China

2 Department mathematics, northwest university, xian, china


In this paper, state operators on hyper BE-algebras (correspondingly, state hyper BE-algebras) are introduced and studied. State hyper filters are introduced and generated state hyper filters are represented in state hyper BE-algebras. Also, maximal (prime) state hyper filters are characterised and the relations between state maximal hyper filters and state prime hyper filters are discussed. Moreover, some related results of state (compatible) hyper congruence are obtained. Especially, it follows that there is an isotone bijection between all state strong regular $\circ$-reflexive hyper filter $\mathcal{F}_s(H,\xi)$ and all state compatible hyper congruence $\mathcal{C}_s(H,\xi)$ on state commutative transitive RD-hyper BE-algebra $(H,\xi)$.