‎Some ‎results ‎on ‎g‎‎raded ‎p‎rime and ‎p‎rimary ‎h‎yperideals

‎Let G be a group with identity e and R be a multiplicative hyperring‎. ‎W‎e introduce the concept of G-graded multiplicative hyperring R and present some ‎new‎ results and examples‎. ‎This ‎‎‎‎‎article ‎aim ‎is ‎‎‎to ‎introduce ‎and ‎study‎ ‎‎‎‎‎‎‎‎‎graded ‎‎prime ‎and  ‎‎graded ‎‎p‎rimary ‎hy‎perideals ‎which ‎are‎ ‎different ‎generalizations ‎of‎ ‎‎prime ‎and‎‎ ‎‎‎‎p‎rimary ‎hyperideals. ‎Several‎ ‎basic  ‎properties‎, ‎examples and characterizations of graded ‎prime (graded ‎primary)‎ hyperideals of a graded multiplicative  hyperring R are ‎presented ‎such ‎as ‎investigating‎ of this structure under homogeneous components‎, ‎graded hyperring  homomorphisms‎, ‎quotient graded hyperrings and fundamental relations‎.