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Edge Ideals and the Cohen-Macaulay Property

Poursoltani Zarandi, Milad | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51358 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Pournaki, Mohammad Reza
  7. Abstract:
  8. set V = {1; : : : ; n}. Let K be a field and let S be the polynomial ring K[x1; : : : ; xn].The edge ideal I(G), associated to G, is the ideal of S generated by the set of squarefree monomials xi xj so that i is adjacent to j. The graph G is Cohen–Macaulay over K if S=I(G) is a Cohen–Macaulay ring. In this project we will explain Herzog-Hibi’s classification of all Cohen–Macaulay bipartite graphs
  9. Keywords:
  10. Edge Ideal ; Bipartite Graph ; Cohen-Macualay Modules ; Polynominal Ring

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