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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 52 Issue: 5

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

Bijan Davvaz(Yazd University)0000-0003-1941-5372
Gülşen Ulucak(GEBZE TECHNICAL UNIVERSITY)0000-0001-6690-6671
Ünsal Tekir(MARMARA UNIVERSITY)0000-0003-0739-1449
Pages
—
Publication Date
2023-10-31
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Finally, we study a version of Nakayama's lemma on a commutative Krasner $ (m,n) $-hyperring.

📌 3 Key Takeaways

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Objective & Hypothesis: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.
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Key Findings & Data:In summary, we give generalizations of $ (k,n) $-absorbing hyperideal and $ (k,n) $-absorbing primary hyperideal.
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Conclusion & Impact:Finally, we study a version of Nakayama's lemma on a commutative Krasner $ (m,n) $-hyperring.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Krasner (m · n)-hyperring · weakly (k

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.

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Cite This Article

Davvaz, B., Ulucak, G., Tekir, Ü. (2023). Weakly $ (k,n) $-absorbing (primary) hyperideals of a Krasner $ (m,n) $-hyperring. Hacettepe Journal of Mathematics and Statistics, Volume: 52 Issue: 5. https://doi.org/10.15672/hujms.1199437

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