The Telescope Conjecture for von Neumann regular rings

Yıl 2024, Cilt: 35 Sayı: 35, 90 - 94, 09.01.2024

Xiaolei Zhang

https://doi.org/10.24330/ieja.1298175

Öz

In this note, we show that any epimorphism originating at a von Neumann regular ring (not necessary commutative) is a universal localization. As an application, we prove that the Telescope Conjecture holds for the unbounded derived categories of von Neumann regular rings (not necessary commutative).

Anahtar Kelimeler

Derived category, ring epimorphism, von Neumann regular ring, the Telescope Conjecture

Kaynakça

• S. Bazzoni and J. Stovicek, Smashing localizations of rings of weak global dimension at most one, Adv. Math., 305 (2017), 351-401.
• A. K. Bousfield, The localization of spectra with respect to homology, Topology, 18(4) (1979), 257-281.
• K. R. Goodearl, von Neumann Regular Rings, Monographs and Studies in Mathematics 4, London, Pitman Publishing, 1979.
• B. Keller, A remark on the generalized smashing conjecture, Manuscripta Math., 84(2)(1994), 193-198.
• H. Krause and J. Stovicek, The telescope conjecture for hereditary rings via Ext-orthogonal pairs, Adv. Math., 225(5) (2010), 2341-2364.
• A. Neeman, The chromatic tower for $D(R)$, Topology, 31(3) (1992), 519-532.
• D. C. Ravenel, Localization with respect to certain periodic homology theories, Amer. J. Math., 160(2) (1984), 351-414.
• J. Saroch and J. Stovicek, The countable Telescope Conjecture for module categories, Adv. Math., 219(3) (2008), 1002-1036.