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Graph Representation of Projective Resolutions 被引量：5

Graph Representation of Projective Resolutions
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摘要 We generalize the concept -- dimension tree and the related results for monomial algebras to a more general case -- relations algebras A by bringing GrSbner basis into play. More precisely, we will describe the minimal projective resolution of a left A-module M as a rooted ＇weighted＇ diagraph to be called the minimal resolution graph for M. Algorithms for computing such diagraphs and applications as well will be presented. We generalize the concept -- dimension tree and the related results for monomial algebras to a more general case -- relations algebras A by bringing GrSbner basis into play. More precisely, we will describe the minimal projective resolution of a left A-module M as a rooted ＇weighted＇ diagraph to be called the minimal resolution graph for M. Algorithms for computing such diagraphs and applications as well will be presented.
作者 Hong Bo SHI
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第3期555-566,共12页 数学学报（英文版）
关键词 Relations algebras dimension trees projective resolutions finitistic dimensions Grobner basis Relations algebras, dimension trees, projective resolutions, finitistic dimensions, Grobner basis
分类号 O185.1 [理学—基础数学] TP311.13 [自动化与计算机技术—计算机软件与理论]
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参考文献10

  • 1Shi, H. B.: Finitistic dimension of monomial algebras. J. Algebra, 264, 397-407 (2003).
  • 2Shi, H. B.: Constructing minimal projective resolutions. Comm. Algebra, 35, 1874-1881 (2007).
  • 3Zimmermann-Huisgen, B.: Predicting syzygies over monomial relations algebras. Manuscripta Math., 70, 157-182 (1991).
  • 4Shi, H. B.: Finitistic Dimension of Monomial Algebras, Doctoral Thesis, University of Toledo, Ohio, 2002.
  • 5Shi, H. B.: Computation of the finitistic dimension of monomial algebras. J. Symbolic Comput, 37, 537-546 (2004).
  • 6Shi, H. B.: Finitistic dimension of dual extension of monomial algebras. Comm. Algebra, 34, 2069-2077 (2006).
  • 7Fenstel, C. D., Green, E. L., Kirkman, E., et al.: Constructing projective resolutions. Comm. Algebra, 21, 1869-1887 (1993).
  • 8Farkas, D. R, Feustel, C. D., Green, E. L.: Synergy in the theories of Gr6bner bases and path algebras. Canad. J. Math., 21, 1869-1887 (1993).
  • 9Xi, C. C.: On the finitistic dimension conjecture I: related to representation-finite algebras. J. Pure Appl. Algebra, 193, 287-305 (2004).
  • 10Xi, C. C.: On the finitistic dimension conjecture II: related to finite global dimension. Adv. Math., 201, 116-142 (2006).

同被引文献10

  • 1王萼芳,石生明.高等代数[M].北京:高等教育出版社,2003.
  • 2B. Buchberger. An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal [ J ]. Journal of Symbolic Computation,2006,41 (3-4) :475 - 511.
  • 3J. C. Faugere. A new efficient algorithm for computing Groebner bases (F4) [ J ]. Journal of Pure and Applied Algebra, 1999,139 (1-3 ) :61 -88.
  • 4J. C. Fangere, P. Gianni, D. Lazard, et al. Efficient computation of zero-dimensional Groebner bases by change of ordering [ J ]. Symbolic Computation, 1993,16 (4) :329 - 344.
  • 5E. A. Arnold. Modular algorithms for computing Groebner bases. [ J ]. Journal of Symbolic Compution,2003,35 (4) :403 - 419.
  • 6D. Cox, J. Little, D. O' Shea. Ideals, Varieties, andAlgorithms [ M ]. New York : Springer-Verlag, 1992.
  • 7M. Sala. Groebner bases and distance of cylie codes[J]. Applicable Algebra in Engineering,Communication and Computing,2002,13(2) :137 - 162.
  • 8D. Farkas, E. Green. Do subspaces have distinguished bases? [ J ]. Rocky Mountain Journal of Mathematics, 1992,22:1295 - 1302.
  • 9张晓燕.有限环上r-MDR码与r-MDS码[J].数学杂志,2011,31(2):376-380. 被引量：1
  • 10吴尽昭.Mechanical Geometry Theorem Proving Based on Groebner Bases[J].Journal of Computer Science & Technology,1997,12(1):10-16. 被引量：1

引证文献5

Acta Mathematica Sinica,English Series
2011年 第3期

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