ABELIAN MODULES

Agayev N., Gungoroglu G., Harmanci A., Halicioglu S.

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, cilt.78, sa.2, ss.235-244, 2009 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 78 Sayı: 2
  • Basım Tarihi: 2009
  • Dergi Adı: ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.235-244
  • Hacettepe Üniversitesi Adresli: Evet

Özet

In this note, we introduce abelian modules as a generalization of abelian rings. Let R be an arbitrary ring with identity. A module M is called abelian if, for any m is an element of M and any a is an element of R, any idempotent e is an element of R, mae = mea. We prove that every reduced module, every symmetric module, every semicommutative module and every Armendariz module is abelian. For an abelian ring R, we show that the module M-R is abelian iff M[x](R[x]) is abelian. We produce an example to show that M[x, alpha] need not be abelian for an abelian module M and an endomorphism alpha of the ring R. We also prove that if the module M is abelian, then M is p.p.-module iff M[x] is p.p.-module, M is Baer module iff M[x] is Baer module, M is p.q.-Baer module iff M[x] is p.q.-Baer module.