Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE FLATNESS AND INJECTIVITY OF DUAL MODULES (III)

  • Published : 2006.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

For a commutative ring R and an injective cogenerator E in the category of R-modules, we characterize von Neumann regular rings and semisimple artinian rings in terms of the properties of dual modules with respect to E.

Keywords

References

  1. T. Albu and C. Nastasescu, Relative Finiteness in Module Theory, Pure and Applied Mathematics (A series of monographs and textbooks) 84, New York: Marcel Dekker, Inc., 1984
  2. F. W. Anderson and K. R. Fuller, Rings and Categories of modules, 2nd ed., Graduate Texts in Mathematics 13, Berlin: Springer-Verlag, 1992
  3. K. A. Byrd, Some characterizations of uniserial rings, Math. Ann. 186 (1970), 163-170 https://doi.org/10.1007/BF01433274
  4. J. S. Golan, Characterization of rings using quasiprojective modules, Israel J. Math. 8 (1970), 34-38 https://doi.org/10.1007/BF02771548
  5. J. S. Golan, Characterization of rings using quasiprojective modules II, Proc. Amer. Math. Soc. 28 (1971), 337-343
  6. P. Griffith, A note on a theorem of Hill, Pacific J. Math. 29 (1969), 279-284 https://doi.org/10.2140/pjm.1969.29.279
  7. Z. Y. Huang, On the flatness and injectivity of dual modules, Southeast Asian Bull. Math. 21 (1997), no. 3, 257-262
  8. Z. Y. Huang and J. Y. Tang, On the flatness and injectivity of dual modules (II), J. Math. Res. Exposition 21 (2001), no. 3, 377-383
  9. T. Ishikawa, Faithfully exact functors and their applications to projective modules and injective modules, Nagoya Math. J. 24 (1964), 29-42 https://doi.org/10.1017/S0027763000011326
  10. J. J. Rotman, An Introduction to Homological Algebra, New York: Academic Press, 1979
  11. B. Stenstrom, Rings of Quotients, Die Grundlehren der Mathematischen Wis-senschaften in Einzeldarstellungen 217, Berlin: Springer-Verlag, 1975