Generalized rigid modules

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GÜNER E., HALICIOĞLU S.

Revista Colombiana de Matematicas, cilt.48, sa.1, ss.111-123, 2014 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 1
  • Basım Tarihi: 2014
  • Doi Numarası: 10.15446/recolma.v48n1.45198
  • Dergi Adı: Revista Colombiana de Matematicas
  • Derginin Tarandığı İndeksler: Scopus, Academic Search Premier, zbMATH, DIALNET
  • Sayfa Sayıları: ss.111-123
  • Anahtar Kelimeler: Armendariz modules, Reduced modules, Rigid module, Semicommutative modules
  • Ankara Üniversitesi Adresli: Evet

Özet

Let α be an endomorphism of an arbitrary ring R with identity. The aim of this paper is to introduce the notion of an α-rigid module which is an extension of the rigid property in rings and the α-reduced property in modules defined in [8]. The class of α-rigid modules is a new kind of modules which behave like rigid rings. A right R-module M is called α-rigid if maα(a) = 0 implies ma = 0 for any m ∈ M and a ∈ R. We investigate some properties of α-rigid modules and among others we also prove that if M[x; α] is a reduced right R[x; α]-module, then M is an α-rigid right R-module. The ring R is α-rigid if and only if every at right R-module is α-rigid. For a rigid right R-module M, M is α-semicommutative if and only if M[x; α]R[x; α] is semicommutative if and only if M [[x; α]]R[[x; α]] is semicommutative.