Rings for which every cyclic module is dual automorphism-invariant

Kosan M. T., Nguyen Thi Thu Ha N. T. T. H., Truong Cong Quynh T. C. Q.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.15, sa.5, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 5
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1142/s021949881650078x
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: (Dual) Automorphism-invariant module and ring, a-ring, q-ring, q*-ring, semiperfect ring
  • Gazi Üniversitesi Adresli: Hayır

Özet

Rings all of whose right ideals are automorphism-invariant are called right a-rings. In the present paper, we study rings having the property that every right cyclic module is dual automorphism-invariant. Such rings are called right a*-rings. We obtain some of the relationships a-rings and a*-rings. We also prove that; (i) A semiperfect ring R is a right a*-ring if and only if any right ideal in J(R) is a left T-module, where T is a subring of R generated by its units, (ii) R is semisimple artinian if and only if R is semiperfect and the matrix ring M-n(R) is a right a*-ring for all n > 1, (iii) Quasi-Frobenius right a*-rings are Frobenius.