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

Authors : Bijan Davvaz, Gülşen Ulucak, Ünsal Tekir

Pages : 1229-1238

Doi:10.15672/hujms.1199437

View : 166 | Download : 235

Publication Date : 2023-10-31

Article Type : Research Paper

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