GENERALIZATIONS OF r-IDEALS OF COMMUTATIVE RINGS

ASLANKARAYİĞİT UĞURLU E.

Journal of Interdisciplinary Mathematics, cilt.24, sa.8, ss.2283-2293, 2021 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 8
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1080/09720502.2021.1876294
  • Dergi Adı: Journal of Interdisciplinary Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.2283-2293
  • Anahtar Kelimeler: r-ideals, phi-prime ideals, phi-r-ideals
  • Marmara Üniversitesi Adresli: Evet

Özet

In this study, we present generalizations of the concept of r-ideals in commutative rings with a nonzero identity. Let R be a commutative ring with 0 not equal 1 and L(R) be the lattice of all ideals of R. Suppose that phi:L(R) -> L(R) boolean OR {circle divide} is a function. A proper ideal I of R is called a phi-r-ideal of R if whenever ab is an element of I and Ann(a) = (0) imply that b is an element of I for each a,b is an element of R. In addition to proven many properties of phi-r-ideals, we also examine the concept of phi-r-ideals in a trivial ring extension and use them to characterize total quotient rings.