研究生: |
李承修 |
---|---|
論文名稱: |
Groebner Bases和Corner Elements的應用:計算Colon Ideals An Application of Groebner Bases and Corner Elements : Computing Colon Ideals |
指導教授: | 劉容真 |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2013 |
畢業學年度: | 101 |
語文別: | 中文 |
論文頁數: | 70 |
中文關鍵詞: | 計算colon ideals |
論文種類: | 學術論文 |
相關次數: | 點閱:114 下載:12 |
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For every even integer n=2k, let q_n be the ideal <x^{2n},y^{2n},(xy+z^2)^n,z^n> in the polynomial ring R=Q[x,y,z]. In her master's thesis [Y], Yao gives a Groebner basis G for q_n and proves that q_n+I_n contain in (q_n:m), where m is the maximal ideal <x,y,z> of R and I_n is the monomial ideal (x^k)(y^k)(z^{2k-1})<x^{2k},y^{2k}><x,y>^{k-1} of R. In this thesis, we prove that (q_n:m) and q_n+I_n are indeed equal. In the process of proving this equality, we give a Groebner basis for the ideals q_n+I_n and find the corner elements of the monomial ideal <LM(q_n)>.
For every even integer n=2k, let q_n be the ideal <x^{2n},y^{2n},(xy+z^2)^n,z^n> in the polynomial ring R=Q[x,y,z]. In her master's thesis [Y], Yao gives a Groebner basis G for q_n and proves that q_n+I_n contain in (q_n:m), where m is the maximal ideal <x,y,z> of R and I_n is the monomial ideal (x^k)(y^k)(z^{2k-1})<x^{2k},y^{2k}><x,y>^{k-1} of R. In this thesis, we prove that (q_n:m) and q_n+I_n are indeed equal. In the process of proving this equality, we give a Groebner basis for the ideals q_n+I_n and find the corner elements of the monomial ideal <LM(q_n)>.
1. David Cox, John Little, and Donal O'shea, Ideals, Varieties, and Algorithms, Springer-Verge, Heidelberg, Berlinm, 1992.
2. L.-M. Li, Some Algorithms of Corner-Elements in Monomial Ideals, master thesis, National Taiwan Normal University, 2007.
3.Y.-T. Yao, An Application of Groebner Bases : Computing the index of reducibility, master thesis, National Taiwan Normal University, 2009.