호남수학학술지 (Honam Mathematical Journal)

  • 제43권3호
  • /
  • Pages.403-416
  • /
  • 2021
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

THE PROJECTIVE MODULE P(2) OVER THE AFFINE COORDINATE RING OF THE 2-SPHERE S2

  • Kim, Sanghee (Department of Mathematics, Chosun University)
  • 투고 : 2021.02.26
  • 심사 : 2021.05.26
  • 발행 : 2021.09.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

It is known that the rank 2 stably free syzygy module P(2) is not free. This algebraic fact was proved analytically, but this remarkable fact still lacks of a simple algebraic proof. The main purpose of this paper is to give a partially algebraic proof by making use of a theorem whose proof is quite topological, and the further properties of the module will be discussed.

키워드

참고문헌

  1. Frank W. Anderson and Kent R. Fuller, Rings and categories of modules, Graduate Texts in Mathematics, Vol. 13, Springer-Verlag, New York-Heidelberg, 1974.
  2. R. Basu and R. Sridharan, On Forster's Conjecture and Related Results, Tata Institute of Fundamental Research, Homi Bhabha Road,Mumbai - 400005
  3. David Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995.
  4. Thomas W. Hungerford, Algebra, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1974.
  5. Friedrich Ischebeck and Ravi A. Rao, Ideals and reality Projective modules and number of generators of ideals, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2005.
  6. Ernst Kunz, Introduction to commutative algebra and algebraic geometry With a preface by David Mumford, Birkhauser Boston, Inc., Boston, MA, Translated from the German by Michael Ackerman, 1985.
  7. T. Y. Lam, Serre's problem on projective modules, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2006.
  8. Satya Mandal, Projective modules and complete intersections, Lecture Notes in Mathematics, vol. 1672, Springer-Verlag, Berlin, 1997.
  9. Donald S. Passman, A course in ring theory, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1991.
  10. R. Y. Sharp, Steps in commutative algebra, London Mathematical Society Student Texts, vol. 19, Cambridge University Press, Cambridge, 1990.
  11. D. W. Sharpe and P. V'amos, Injective modules, Cambridge University Press, London-New York, Cambridge Tracts in Mathematics and Mathematical Physics, No. 62, 1972.
  12. Masahisa Sato, Some Examples of Rings and Modules and Application to Ware's Problem II, Summer School on Ring and Module Theory 2019, Chungnam National University, Daejeon, South Korea, July 29-31, 2019.
  13. Ihsen Yengui, Constructive commutative algebra Projective modules over polynomial rings and dynamical Grobner bases, Lecture Notes in Mathematics, vol. 2138, Springer, Cham, 2015.