Chain Condition and Fundamental Relation on (∆;G)-Sets Derived from Gamma-Semihypergroups
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Authors: S. OSTADHADI-DEHKORDI
DOI: 10.46793/KgJMat2101.021O
Abstract:
The aim of this research work is to define a new class of hyperstructure as a generalization of semigroups, semihypergroups and Γ-semihypergroups that we call (Δ,G)-sets. Also, we define fundamental relation on (Δ,G)-sets and prove some results in this respect. Then, we introduce the notions of quotient (Δ,G)-sets by using a congruence relations. Finally, we introduce the concept of complete parts and Noetherian(Artinian) (Δ,G)-sets.
Keywords:
Γ-semihypergroup, left(right) (Δ,G)-set, twist product, flat Γ-semihypergroup, absolutely flat Γ-semihypergroup.
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