# Questions tagged [monomial-order]

A monomial order is a total order on the set of all (monic) monomials in a given polynomial ring, satisfying the property of respecting multiplication.

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### An infinity of monomial order on $K[x,y]$ [closed]

I must prove that there are an infinity of monomial orders on $K [x, y]$. But I don't know where to start the demonstration
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### Monomial order in $K[x,y]$

I'm learning abstract algebra and came across the following statement: In the ring $K [x,y]$ there is exactly a monomial order $≤$ with property as $y^i <x$ for any $i ≥ 2$. I'm thinking of ...
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### Complete Intersection ideal whose initial ideal is not even Cohen-Macaulay

I am trying to find an example, such a example is asked in exercise 3.3 of the book Monomial Ideals (Herzog & Hibi). I would like to find a graded ideal $I\subset k[x_1,\cdots,x_n]$ which is ...
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Let $k$ be a field and let $f\in k[X_1,\ldots,X_n]$ be a polynomial. Write $$f = \sum_\alpha \underline{X}^{\underline{\alpha}}\qquad \underline{X}^{\underline{\alpha}} \text{ is a monomial in }X_1,\... 1answer 50 views ### Need help in understanding definition of monomials Wikipedia states two definitions of monomials- https://en.m.wikipedia.org/wiki/Monomial I have understood the first one but I am facing some problem in understanding the second one which says that-" ... 1answer 125 views ### A question about extending polynomial span to monomial basis I have a final next week and our instructor gave us some examples with solutions but I could not understand some operations. Inner product is$$(p,q)=\int_{-1}^{1} p(t)q(t)dt $W = Span\{1,t,t^2\}$ ...
Suppose I am working in a polynomial ring in several variables, say $k[X]=k[x_1,\dots, x_n]$. An ordering $<$ on $k[X]$ is said to be degree compatible, if: \$\deg(X^u)<\deg(X^v) \implies X^u <...