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Let $K[x_1,...,x_n]$ be the polynomial ring in $n$ variables and $a_1,...,a_m$ elements in the quotient field $K(x_1,...,x_n)$. Let $A:=K[a_1,...,a_m]$ the ring generated by the $a_i$ in $K(x_1,...,...

Let $R$ be a quotient of the polynomial ring $\mathbb{C}[x_1,\dots , x_n]$. We fix a $\mathbb{C}^*$ action on $R$ which preserve homogenous components and the multiplication. (The geometric analogue ...

Any reference or suggestion for the following problem would be greatly appreciated. I am working on the quotient ring $Q=R[X_1,\dots,X_n]/<f_1,\dots,f_k>$. Given polynomials $p$ and $q$ I want ...