DOI QR코드

DOI QR Code

LOCAL SPLITTING PROPERTIES OF ENDOMORPHISM RINGS OF PROJECTIVE MODULES

  • Lee, Sang Cheol (Department of Mathematics Education and Institute of Pure and Applied Mathematics, Chonbuk National University)
  • Received : 2013.10.14
  • Accepted : 2013.11.22
  • Published : 2013.12.25

Abstract

This paper deals with the unit groups of the endomorphism rings of projective modules over polynomial rings and further over formal power series rings. A normal subgroup of the unit group is defined and discussed. The local splitting properties of element of endomorphism rings of projective modules over polynomial rings are given.

Keywords

References

  1. S. M. Bhatwadekar and Raja Sridharan, The Euler Class Group of a Noetherian Ring, Composito Mathematica, 122 (2000), 183-222. https://doi.org/10.1023/A:1001872132498
  2. R. Basu and R. Sridharan, On Forster's Conjecture and Related Results, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400005, India, 2002.
  3. F. Ischebeck and Ravi Rao, Ideals and Reality, Projective Modules and Number of Generators of Ideals, Springer, 2005.
  4. S. Mandal, Projective Modules and Complete Intersections, Springer, 1997.
  5. D. Quillen, Projective Modules over Polynomial Rings, Inv. Math. 36 (1976), 167-171. https://doi.org/10.1007/BF01390008
  6. S. Raghavan Balwant Singh and R. Sridharan, Homological Methods in Commutative Algebra, Tata Institute of Fundamental Research, Bombay, 1975.