phi-Classical Prime Submodules

Mostafanasab H., Ugurlu E. A.

SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, cilt.43, sa.2, ss.243-262, 2019 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 2
  • Basım Tarihi: 2019
  • Dergi Adı: SOUTHEAST ASIAN BULLETIN OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.243-262
  • Anahtar Kelimeler: Classical prime submodule, Weakly classical prime submodule, phi-Classical prime submodule, MODULES
  • Marmara Üniversitesi Adresli: Evet

Özet

In this paper, all rings are commutative with nonzero identity. Let M be an R-module. A proper submodule N of M is called a classical prime submodule, if for each m is an element of M and elements a, b is an element of R, abm is an element of N implies that am is an element of N or bm is an element of N. Let phi : S(M) -> S(M) U {empty set} be a function where S(M) is the set of all submodules of M. We introduce the concept of "phi-classical prime submodules". A proper submodule N of M is a phi-classical prime submodule if whenever a, b is an element of R and m is an element of M with abm is an element of N\phi(N), then am is an element of N or bm is an element of N.