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Year 2024, Volume: 35 Issue: 35, 90 - 94, 09.01.2024
https://doi.org/10.24330/ieja.1298175

Abstract

References

  • 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.

The Telescope Conjecture for von Neumann regular rings

Year 2024, Volume: 35 Issue: 35, 90 - 94, 09.01.2024
https://doi.org/10.24330/ieja.1298175

Abstract

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).

References

  • 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.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Xiaolei Zhang This is me

Early Pub Date May 24, 2023
Publication Date January 9, 2024
Published in Issue Year 2024 Volume: 35 Issue: 35

Cite

APA Zhang, X. (2024). The Telescope Conjecture for von Neumann regular rings. International Electronic Journal of Algebra, 35(35), 90-94. https://doi.org/10.24330/ieja.1298175
AMA Zhang X. The Telescope Conjecture for von Neumann regular rings. IEJA. January 2024;35(35):90-94. doi:10.24330/ieja.1298175
Chicago Zhang, Xiaolei. “The Telescope Conjecture for Von Neumann Regular Rings”. International Electronic Journal of Algebra 35, no. 35 (January 2024): 90-94. https://doi.org/10.24330/ieja.1298175.
EndNote Zhang X (January 1, 2024) The Telescope Conjecture for von Neumann regular rings. International Electronic Journal of Algebra 35 35 90–94.
IEEE X. Zhang, “The Telescope Conjecture for von Neumann regular rings”, IEJA, vol. 35, no. 35, pp. 90–94, 2024, doi: 10.24330/ieja.1298175.
ISNAD Zhang, Xiaolei. “The Telescope Conjecture for Von Neumann Regular Rings”. International Electronic Journal of Algebra 35/35 (January 2024), 90-94. https://doi.org/10.24330/ieja.1298175.
JAMA Zhang X. The Telescope Conjecture for von Neumann regular rings. IEJA. 2024;35:90–94.
MLA Zhang, Xiaolei. “The Telescope Conjecture for Von Neumann Regular Rings”. International Electronic Journal of Algebra, vol. 35, no. 35, 2024, pp. 90-94, doi:10.24330/ieja.1298175.
Vancouver Zhang X. The Telescope Conjecture for von Neumann regular rings. IEJA. 2024;35(35):90-4.