DOI QR코드

DOI QR Code

INJECTIVE COVERS OVER COMMUTATIVE NOETHERIAN RINGS WITH GLOBAL DIMENSION AT MOST TWO

  • Published : 2003.02.01

Abstract

In [3], Del Valle, Enochs and Martinez studied flat envelopes over rings and they showed that over rings as in the title these are very well behaved. If we replace flat with injective and envelope with the dual notion of a cover we then have the injective covers. In this article we show that these injective covers over the commutative noetherian rings with global dimension at most 2 have properties analogous to those of the flat envelopes over these rings.

Keywords

injective cover

References

  1. Math. Z. v.82 On the ubiquity of Gorenstein rings H. Bass https://doi.org/10.1007/BF01112819
  2. J. Algebra v.134 Stable equivalence of self-injective algebras and a generalization of tilting modules T. Wakamatsu https://doi.org/10.1016/0021-8693(90)90055-S
  3. Homotopy theory and duality P. Hilton
  4. Pacific J. Math. v.8 Injective modules over Noetherian rings E. Matlis https://doi.org/10.2140/pjm.1958.8.511
  5. Proc. Amer. Math. Soc. v.126 Coherent rings of finite weak flobal dimension E. Enochs;J. Martinez Hernandez;A. Del Valle https://doi.org/10.1090/S0002-9939-98-04191-4
  6. Israel J. Math. v.39 Injective and flat covers, envelopes, and resolvents E. Enochs https://doi.org/10.1007/BF02760849
  7. Lecture Notes in Math. v.1634 Flat Covers of Modules J. Xu