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Adds link to wiki definition of numerical semigroup
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Luc Guyot
Luc Guyot
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Canonical module of a semigroup ring

Let $S$ be a numerical semigroupnumerical semigroup and $k[S]$ is the associated semigroup ring. I would like to compute canonical module $\omega$ of $k[S].$

I want to show that $\omega=k[t^{-n}:n\in\mathbb Z\setminus S]$.

I have shown that $H^1_{m}(k[S])=k[t^{n}:n\in\mathbb Z\setminus S]$ where $m$ is the maximal homogeneous ideal of $k[S].$ Using duality I tried to compute canonical ideal but I am not able to do it.

Canonical module of semigroup ring

Let $S$ be a numerical semigroup and $k[S]$ is the associated semigroup ring. I would like to compute canonical module $\omega$ of $k[S].$

I want to show that $\omega=k[t^{-n}:n\in\mathbb Z\setminus S]$.

I have shown that $H^1_{m}(k[S])=k[t^{n}:n\in\mathbb Z\setminus S]$ where $m$ is the maximal homogeneous ideal of $k[S].$ Using duality I tried to compute canonical ideal but I am not able to do it.

Canonical module of a semigroup ring

Let $S$ be a numerical semigroup and $k[S]$ is the associated semigroup ring. I would like to compute canonical module $\omega$ of $k[S].$

I want to show that $\omega=k[t^{-n}:n\in\mathbb Z\setminus S]$.

I have shown that $H^1_{m}(k[S])=k[t^{n}:n\in\mathbb Z\setminus S]$ where $m$ is the maximal homogeneous ideal of $k[S].$ Using duality I tried to compute canonical ideal but I am not able to do it.

Notice added Draw attention by Cusp
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Cusp
Cusp
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Canonical module of semigroup ring

Let $S$ be a numerical semigroup and $k[S]$ is the associated semigroup ring. I would like to compute canonical module $\omega$ of $k[S].$

I want to show that $\omega=k[t^{-n}:n\in\mathbb Z\setminus S]$.

I have shown that $H^1_{m}(k[S])=k[t^{n}:n\in\mathbb Z\setminus S]$ where $m$ is the maximal homogeneous ideal of $k[S].$ Using duality I tried to compute canonical ideal but I am not able to do it.