대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제21권4호
  • /
  • Pages.613-630
  • /
  • 2006
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

g등급 완전 아이디얼의 구조정리

  • 발행 : 2006.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

noetherian 국소 가환환에서 g등급 완전 아이디얼의 성질과 구조를 조사한다. 완전행렬과 일반화된 교대행렬를 이용하여 3 등급 완전아이디얼의 구조를 새롭게 밝힌다.

키워드

참고문헌

  1. E. Artin, Geometric algebra, Interscience Tracts in Pure and Appl. Math, vol 3 Interscience London, 1957
  2. L. Avramov, Obstructions to the existence of multiplicative structures on minimal free resolutions, Amer. J. Math. 103 (1981), 1-31 https://doi.org/10.2307/2374187
  3. L. Avramov, A. Kustin, and M. Miller, Poincare series of modules over local rings of small embedding codepth or small linking number, J. Algebra 118 (1988), 162-204 https://doi.org/10.1016/0021-8693(88)90056-7
  4. D. A. Buchsbaum and D. Eisenbud, What makes the complex exact ?, J. Algebra 25 (1973), 259-268 https://doi.org/10.1016/0021-8693(73)90044-6
  5. D. A. Buchsbaum and D. Eisenbud, Algebra structures for finite free resolutions and some structure theorems for ideals of codimension 3, Amer. J. Math. 99 (1977), no. 3, 447-485 https://doi.org/10.2307/2373926
  6. A. Brown, A structure theorem for a class of grade three perfect ideals, J. Algebra 105 (1987), 308-327 https://doi.org/10.1016/0021-8693(87)90196-7
  7. L. Burch, On ideals of finite homological dimension in local rings, Proc. Cambridge Philos. Soc. 64 (1968), 941-948
  8. E. S. Golod, A note on perfect ideals, from the collection 'Algebra'(A. I. Kostrikin, Ed) Moscow State Univ. Publishing House (1980) 37-39
  9. A. Kustin, Gorenstein algebras of codimension four and characteristic two, Comm. Alg. 15 (1987), 2417-2429 https://doi.org/10.1080/00927878708823544
  10. A. Kustin, The minimal resolution of a codimension four almost complete intersec-tion is DGC-algebra, J. Algebra 168 (1994), no. 2, 371-399 https://doi.org/10.1006/jabr.1994.1235
  11. O.-J. Kang and H. J. Ko, The structure theorem for Complete Intersections of grade 4, Algebra Collo. 12 (2005), no. 2, 181-197 https://doi.org/10.1142/S1005386705000179
  12. A. Kustin and M. Miller, Algebra Structures on Minimal free resolutions of Gorenstein Rings of Embedding Codimension four, Math. Z. 173 (1980), 171-184 https://doi.org/10.1007/BF01159957
  13. A. Kustin and M. Miller, Structure theory for a class of grade four Gorenstein ideals, Trans. Amer. Math. Soc. 270 (1982), 287-307 https://doi.org/10.2307/1999773
  14. A. Kustin and M. Miller, Multiplication structure on resolutions of algebras defined by Herzog ideals, J. London Math. Soc. 28 (1983), no. 2, 247-260 https://doi.org/10.1112/jlms/s2-28.2.247
  15. E. Kunz, Almost complete intersections are not Gorenstein, J. algebra. 28 (1974), 111-115 https://doi.org/10.1016/0021-8693(74)90025-8
  16. S. Palmer, Multiplication Structure on resolutions of grade four almost complete intersections, J. Algebra 159 (1993), no. 1, 1-46 https://doi.org/10.1006/jabr.1993.1144
  17. C. Peskine and L. Szpiro, Liaison des uarietes alqebriques , Invent. Math. 26 (1974), 271-302 https://doi.org/10.1007/BF01425554
  18. R. Sanchez, A Structure Theorem for Type 3, Grade 3 Perfect Ideals, J. Algebra 123 (1989), 263-288 https://doi.org/10.1016/0021-8693(89)90047-1
  19. J.-P. Serre, Sur les modules projectifs, Seminaire Dubreil, (1960)
  20. H. Srinivasan, Algebra Structures on some canoncal resolutions, J. Algebra 122 (1989), 150-187 https://doi.org/10.1016/0021-8693(89)90244-5
  21. H. Srinivasan, Minimal algebra resolutions for cyclic modules defined by Huneke- Ulrich ideal, J. Algebra 137 (1991), 433-472 https://doi.org/10.1016/0021-8693(91)90101-D
  22. H. Srinivasan, A Grade Five Gorenstein Algebra with no Minimal Algebra resolutions, J. Algebra 179 (1996), 362-372 https://doi.org/10.1006/jabr.1996.0016
  23. R. P. Stanley, Hilbert functions of graded algebras, Adv. in Math. 28 (1978), 57-83 https://doi.org/10.1016/0001-8708(78)90045-2

피인용 문헌

  1. The Structure for Some Classes of Grade Three Perfect Ideals vol.39, pp.9, 2011, https://doi.org/10.1080/00927872.2010.512586
  2. PERFECT IDEALS OF GRADE THREE DEFINED BY SKEW-SYMMETRIZABLE MATRICES vol.49, pp.4, 2012, https://doi.org/10.4134/BKMS.2012.49.4.715