2-absorbing phi-delta-primary ideals

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Yavuz S., ONAR S., ERSOY B. A., TEKİR Ü., KOÇ S.

TURKISH JOURNAL OF MATHEMATICS, cilt.45, ss.1927-1939, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3906/mat-2105-21
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1927-1939
  • Anahtar Kelimeler: 2-absorbing ideal, 2-absorbing primary ideal, 2-absorbing phi-delta-primary ideal
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Marmara Üniversitesi Adresli: Evet

Özet

This paper aims to introduce 2-absorbing phi-delta-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 delta : I(A) -> I(A) is an expansion function and phi : I(A) -> I(A)U{theta} is a reduction function. A proper ideal Q of A is said to be a 2-absorbing phi-delta-primary if whenever abc is an element of Q - phi(Q), where a, b, c is an element of R, then either ab is an element of Q or ac is an element of delta(Q) or bc is an element of delta(Q). Various examples, properties, and characterizations of this new class of ideals are given.