Rings whose RD-flat modules have restricted subflat domains

DURĞUN Y., Bozkurt M.

Rendiconti del Circolo Matematico di Palermo, cilt.73, sa.2, ss.579-585, 2024 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 73 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s12215-023-00928-x
  • Dergi Adı: Rendiconti del Circolo Matematico di Palermo
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.579-585
  • Anahtar Kelimeler: 16D10, 18G25, f-Test module, RD-flat module, tf-Test module, Torsion-free module
  • Çukurova Üniversitesi Adresli: Evet

Özet

A module KR is said to be RL-subflat if for every short exact sequence 0→U→D→L→0 of left R-modules, the sequence 0→K⊗U→K⊗D→K⊗L→0 is exact. The subflat domains of (RD-flat) modules somehow tells us how far (or how close) such a module is from being flat. Every right R-module is subflat relative to all flat left R-modules, and flat modules are the only ones sharing the distinction of being in every single subflat domain. A module is called f-test if it is subflat only to flat modules. Similarly, an RD-flat module is called tf-test if it is subflat only to torsion-free modules. In this paper, we consider two families of rings characterized by their RD-flat modules: those whose finitely presented RD-flat modules are either flat or tf-test (property (P)) and those whose finitely presented RD-flat modules are either torsion-free (flat) or f-test (property (Q)). Structural properties of both classes of rings are studied.