On Automorphism-Invariant Rings with Chain Conditions

Truong Cong Quynh T. C. Q., KOŞAN M. T., Le Van Thuyet L. V. T.

VIETNAM JOURNAL OF MATHEMATICS, cilt.48, sa.1, ss.23-29, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s10013-019-00336-8
  • Dergi Adı: VIETNAM JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.23-29
  • Gazi Üniversitesi Adresli: Evet

Özet

It is shown that if R is a right automorphism-invariant ring and satisfies ACC on right annihilators, then R is a semiprimary ring. By this useful fact, we study finiteness conditions which ensure an automorphism-invariant ring is quasi-Frobenius (QF). Thus, we prove, among other results, that: (1) R is QF if and only if R is right automorphism-invariant, right min-CS and satisfies ACC on right annihilators; (2) R is QF if and only if R is left Noetherian, right automorphism-invariant and every complement right ideal of R is a right annihilator; (3) If R is right CPA, right automorphism-invariant and every complement right ideal of R is a right annihilator, then R is QF.