A look at FPF rings

Ghashghaei E., KOŞAN M. T., Quynh T. C., Van Thuyet L.

Journal of Algebra and its Applications, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1142/s0219498825501609
  • Dergi Adı: Journal of Algebra and its Applications
  • 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: Baer ring, FPF ring, II-coherent ring, II-semihereditary ring, ring of continuous functions
  • Gazi Üniversitesi Adresli: Evet

Özet

An error in Corollary 9.32 of [C. Faith, Rings and Things and a Fine Array of Twentieth Century Associative Algebra, Mathematical Surveys and Monographs, Vol. 65 (American Mathematical Society, Providence, RI, 2004)], motivated us to consider again FPF rings which were initiated by Faith in the 1970s. In this paper, it is shown that a commutative ring R is reduced FPF if and only if it is II-semihereditary. We show that when a semiperfect ring with a strongly right bounded basic ring with right and left Ore conditions, is an FPF ring. After some general results, the article focuses on rings of continuous functions. We give some algebraic characterizations for a C(X) to be FPF and retrieve a result of Jorge Martinez. Also, we show that a space X is fraction-dense if and only if Qcl(X) is a continuous ring.