On Semicommutative Modules and Rings

Agayev N., Harmanci A.

KYUNGPOOK MATHEMATICAL JOURNAL, cilt.47, sa.1, ss.21-30, 2007 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 1
  • Basım Tarihi: 2007
  • Dergi Adı: KYUNGPOOK MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.21-30
  • Hacettepe Üniversitesi Adresli: Evet

Özet

We say a module M R a semicommutative module if for any m 2 M and any a epsilon R, ma = 0 implies mRa = 0. This paper gives various properties of reduced, Armendariz, Baer, Quasi-Baer, p.p . and p.q .-Baer rings to extend to modules. In addition we also prove, for a p. p.-ring R, R is semicommutative iff R is Armendariz. Let R be an abelian ring and M-R be a p.p.-module, then M-R is a semicommutative module iff M-R is an Armendariz module. For any ring R, R is semicommutative iff A (R,alpha) is semicommutative. Let R be a reduced ring, it is shown that for number n >= 4 and k = [n = 2]; T-n(k) (R) is semicommutative ring but T-n(k-1) (R) is not.