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

Year 2023, Volume: 52 Issue: 5, 1229 - 1238, 31.10.2023

Bijan Davvaz , Gülşen Ulucak , Ünsal Tekir

https://doi.org/10.15672/hujms.1199437

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

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