Kyungpook Mathematical Journal

  • 제64권2호
  • /
  • Pages.197-204
  • /
  • 2024
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

Minimal Generators of Syzygy Modules Via Matrices

  • Haohao Wang (Department of Mathematics, Southeast Missouri State University) ;
  • Peter Oman (Department of Mathematics, Southeast Missouri State University)
  • 투고 : 2023.04.20
  • 심사 : 2024.03.10
  • 발행 : 2024.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Let R = 𝕂[x] be a univariate polynomial ring over an algebraically closed field 𝕂 of characteristic zero. Let A ∈ Mm,m(R) be an m×m matrix over R with non-zero determinate det(A) ∈ R. In this paper, utilizing linear-algebraic techniques, we investigate the relationship between a basis for the syzygy module of f1, . . . , fm and a basis for the syzygy module of g1, . . . , gm, where [g1, . . . , gm] = [f1, . . . , fm]A.

키워드

참고문헌

  1. W. A. Adkins and S. H. Weintraub, Algebra, Graduate Texts in Mathematics, Springer-Verlag, 1992.
  2. V. A. Bovdi and L. A. Kurdachenko, Modules over some group rings, having dgenerator property, Ric. Mat., 71(2022), 135-145. https://doi.org/10.1007/s11587-021-00581-5.
  3. D. Cox, J. Little and D. O'shea, Using Algebraic Geometry, Graduate Texts in Mathematics Vol. 185, Springer, New York, 2005
  4. D. E. Dobbs, On minimal generating sets of modules over a special principal ideal ring, Lecture Notes in Pure and Appl. Math, Dekker, New York, 185(1997), 241-250.
  5. D. Eisenbud, Commutative algebra. With a view toward algebraic geometry, Graduate Texts in Mathematics Vol. 150, Springer-Verlag, New York, 1995.
  6. D. T. Gu'e, Minimum number of generators of the lattice of submodules of a semisimple module, J. Sov. Math., 30(1985), 1872-1874.
  7. D. Hilbert, Ueber die Theorie der algebraischen Formen, Math. Ann., 36(1890), 473-534.
  8. A. A. Kravchenko, On the minimum number of generators of the lattice of subspaces of a finite dimensional linear space over a finite field, J. Sov. Math., 27(1984), 2942-2943.