Some Aspects of Hyperatom Elements in Ordered Semihyperrings

Abstract

In this paper, first, we state an operator LR on an ordered semihyperring R. We show that if φ:R⟶T is a monomorphism and K⊆R, then LT(φ(K))=φ(LR(K)). Afterward, hyperatom elements in ordered semihyperrings are defined and some results in this respect are investigated. Denote by A(R) the set of all hyperatoms of R. We prove that if R is a finite ordered semihyperring and |R|≥2, then for any q∈R\{0}, there exists hq∈A*(R)=A(R)\{0} such that hq≤q. Finally, we study the LR-graph of an ordered semihyperring and give some examples. Furthermore, we show that if φ:R⟶T is an isomorphism, G is the LR-graph of R and G′ is the LT-graph of T, then G≅G′.