On rings all of whose right ideals are automorphism-invariant

Tien N. Q., Truong Cong Q., KOŞAN M. T.

Communications in Algebra, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1080/00927872.2024.2447493
  • Dergi Adı: Communications in Algebra
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Automorphism-invariant module, a-ring, q-ring, self-injective ring
  • Gazi Üniversitesi Adresli: Evet

Özet

Rings all of whose right ideals are automorphism-invariant are called right a-rings. It is shown that (Formula presented.) local right a-rings are left duo, (Formula presented.) local rings whose left ideals of R are invariant under all units of R are left duo, (Formula presented.) a right a-ring R with (Formula presented.) is duo. In this paper, the question of when is a left a-ring a right a-ring is also addressed. It is shown that (Formula presented.) if R is a quasi-Frobenius ring or right (or left) noetherian/artinian ring, then R is a right a-ring if and only if R is a left a-ring. It is also proved that (Formula presented.) R is a right a-ring with ACC on right annihilators iff R is a left a-ring with ACC on left annihilators, questions (partially) answering the different question on this topic.