NOTES ON THE REGULAR MODULES

  • Published : 1999.11.01

Abstract

It is a well-known result that a commutative ring R is von Neumann regular if and only if for any maximal ideal m of R the R-module R/m is flat. In this note we bring a generalization of this result for modules.

Keywords

References

  1. Commutative algebra N. Bourbaki
  2. Pacific J. Math. v.65 no.2 Regular and semisimple modules T. J. Cheatham;J. R. Smith
  3. Proc. Amer. Math. Soc. v.81 no.2 Flat and projective character modules T. J. Cheatham;D. R. Stone
  4. Ph. D. Thesis, McGill University Purity and flatness D. J. Fiedhouse
  5. Lecture notes in Math. v.1371 Commutative coherent rings S. Glaz
  6. Von Neumann regular rings K. R. Goodearl
  7. Commutative ring theory H. Matsumura
  8. An introduction to homological algebra J. Rotman
  9. J. London Math. Soc. v.2 no.2 Coherent rings and FP-injective modules B. Stenstrom
  10. Commun. in Algebra v.19 no.2 Flatness and injectivity of simple modules over a commutative ring J. Xu