weakly $ (k,n) $-absorbing (primary) hyperideals of a Krasner $ (m,n) $-hyperring

In this paper, we introduce new expansion classes, namely weakly $ (k,n) $-absorbing hyperideals and primary of a Krasner (m,n) $-hyperring, including hyperideal hyperideal. Therefore, give generalizations Also, examine the relations between classical explore some ways to connect them. Additionally, main results examples are given explain structures these concepts. Finally, study version Nakayama's lemma on commutative $-hyperring.