On weakly 2-prime ideals in commutative rings

KOÇ S.

Communications in Algebra, cilt.49, ss.3387-3397, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1080/00927872.2021.1897133
  • Dergi Adı: Communications in Algebra
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.3387-3397
  • Anahtar Kelimeler: Compactly 2-packed ring, compactly packed ring, coprimely packed ring, 2-prime ideal, weakly 2-prime ideal, weakly prime ideal
  • Marmara Üniversitesi Adresli: Evet

Özet

© 2021 Taylor & Francis Group, LLC.The purpose of the paper is to introduce and study weakly 2-prime ideals in commutative rings. Let A be a commutative ring with a nonzero identity. A proper ideal P of A is said to be a weakly 2-prime ideal if whenever (Formula presented.) for some (Formula presented.) then (Formula presented.) or (Formula presented.) Besides giving various examples and characterizations of weakly 2-prime ideals, we investigate the relations between weakly 2-prime ideals and other classical ideals such as 2-prime ideals, weakly prime ideals and weakly 2-absorbing primary ideals. Furthermore, we study 2-prime avoidance lemma in commutative rings and introduced the class of compactly 2-packed rings. Finally, we investigate the compactly packedness, compactly 2-packedness and coprimely packedness of trivial extension (Formula presented.) of an A-module M.