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Thomas Kahle
Thomas Kahle
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Let $S=k[x_1,\dots,x_n]$ be a polynomial ring, and $A:=k[x^{u^{(1)}}, \dots x^{u^{(l)}}]$ a monomial subalgebra, generated by monomials $x^{u^{(i)}} = \prod_{j=1}^n x_j^{u^{(i)}_{j}}$ with $u^{(i)} \in \mathbf{N}^n$. What are sufficient criteria for the inclusion $0\to A \to S$$A \to S$ to split? What is the splitting? Since S is normal, and direct summands of normal rings are normal, normality of A is necessary.

Let $S=k[x_1,\dots,x_n]$ be a polynomial ring, and $A:=k[x^{u^{(1)}}, \dots x^{u^{(l)}}]$ a monomial subalgebra, generated by monomials $x^{u^{(i)}} = \prod_{j=1}^n x_j^{u^{(i)}_{j}}$ with $u^{(i)} \in \mathbf{N}^n$. What are sufficient criteria for the inclusion $0\to A \to S$ to split? What is the splitting? Since S is normal, and direct summands of normal rings are normal, normality of A is necessary.

Let $S=k[x_1,\dots,x_n]$ be a polynomial ring, and $A:=k[x^{u^{(1)}}, \dots x^{u^{(l)}}]$ a monomial subalgebra, generated by monomials $x^{u^{(i)}} = \prod_{j=1}^n x_j^{u^{(i)}_{j}}$ with $u^{(i)} \in \mathbf{N}^n$. What are sufficient criteria for the inclusion $A \to S$ to split? What is the splitting? Since S is normal, and direct summands of normal rings are normal, normality of A is necessary.

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Thomas Kahle
Thomas Kahle
  • 2k
  • 15
  • 29

Which monomial subalgebras are direct summands of polynomial rings

Let $S=k[x_1,\dots,x_n]$ be a polynomial ring, and $A:=k[x^{u^{(1)}}, \dots x^{u^{(l)}}]$ a monomial subalgebra, generated by monomials $x^{u^{(i)}} = \prod_{j=1}^n x_j^{u^{(i)}_{j}}$ with $u^{(i)} \in \mathbf{N}^n$. What are sufficient criteria for the inclusion $0\to A \to S$ to split? What is the splitting? Since S is normal, and direct summands of normal rings are normal, normality of A is necessary.