Chain Condition and Fundamental Relation on $(\Delta,G)$-Sets Derived from $\Gamma$-semihypergroups

S. Ostadhadi-Dehkordi

The aim of this research work is to define a new class of hyperstructure as a generalization of semigroups, semihypergroups and $\Gamma$-semihypergroups that we call $(\Delta,G)$-sets. Also, we define fundamental relation on $(\Delta,G)$-sets and prove some results in this respect. Then, we introduce the notions of quotient $(\Delta,G)$-sets by using a congruence relations. Finally, we introduce the concept of complete parts and Noetherian(Artinian) $(\Delta,G)$-sets.