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Journals / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 4

$beta$-relations on implicative bounded hyper BCK-algebras

S. RASOULI
D. HEIDARI
B. DAVVAZ
Pages
461–469
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we state conditions that are equivalent with the transitivity of this relation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we consider the notion of hyper implicative bounded BCK- algebras, give some examples and introduce the relation $beta$ on them.
📊
Key Findings & Data:Then we let $beta^∗$ be the transitive closure of $beta$ .
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Conclusion & Impact:Finally, we state conditions that are equivalent with the transitivity of this relation.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper we consider the notion of hyper implicative bounded BCK- algebras, give some examples and introduce the relation $beta$ on them. Then we let $beta^∗$ be the transitive closure of $beta$ . In hyper implicative bounded BCK-algebra theory, the fundamental relation is defined as the smallest equivalence relation so that the quotient would be the (fundamental) BCK-algebra. We show that$beta^∗$ is the fundamental re- lation on a hyper implicative bounded BCK-algebra. Finally, we state conditions that are equivalent with the transitivity of this relation.

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Cite This Article

RASOULI, S., HEIDARI, D., DAVVAZ, B. (2022). $beta$-relations on implicative bounded hyper BCK-algebras. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 4, 461–469. https://ajindex.com/articles/530674

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References (9)

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