Fatemeh Arabpur - Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
Morteza Jafarpour - Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

This paper generalizes the idea of strongly associative hyperoperation introduced in [7]  to the class of hyperrings. We introduce and investigate hyperrings of type 1, type 2 and SDIS. Moreover, we study some examples of these hyperrings and give a new kind of hyperrings called  totally hyperrings. Totally hyperrings give us a characterization of Krasner hyperrings. Also, we investigate these strongly hyperoperations in hyperring of series.

‎Strongly associative hyperoperation‎, ‎SDIS hyperring‎, ‎Krasner hyperring‎, ‎totally hyperring‎, ‎hyperring of series‎