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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Various examples, properties, and characterizations of this new class of ideals are given.
📌 3 Key Takeaways
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Objective & Hypothesis:This paper aims to introduce 2-absorbing φ-δ -primary ideals over commutative rings which unify the concepts of all generalizations of 2-absorbing and 2-absorbing primary ideals.
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Key Findings & Data:A proper ideal Q of A is said to be a 2-absorbing φ-δ -primary if whenever abc ∈ Q − φ(Q), where a, b, c ∈ R, then either ab ∈ Q or ac ∈ δ(Q) or bc ∈ δ(Q).
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Conclusion & Impact:Various examples, properties, and characterizations of this new class of ideals are given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
This paper aims to introduce 2-absorbing φ-δ -primary ideals over commutative rings which unify the concepts of all generalizations of 2-absorbing and 2-absorbing primary ideals. Let A be a commutative ring with a nonzero identity and I(A) be the set of all ideals of A. Suppose that δ : I(A) → I(A) is an expansion function and φ : I(A) → I(A)∪{∅} is a reduction function. A proper ideal Q of A is said to be a 2-absorbing φ-δ -primary if whenever abc ∈ Q − φ(Q), where a, b, c ∈ R, then either ab ∈ Q or ac ∈ δ(Q) or bc ∈ δ(Q). Various examples, properties, and characterizations of this new class of ideals are given.
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Cite This Article
ONAR, S., ERSOY, B. A., YAVUZ, S., KOÇ, S., TEKİR, Ü. (2022). 2-absorbing φ-δ -primary ideals. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 5, 1927–1939. https://ajindex.com/articles/607800