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The word normalization refers to a procedure transforming an algebraic variety (more generally, a scheme) to a normal one via a birational morphism. This tag should be used only for questions in algebraic geometry rather than ones in analysis, logic or probability.

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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)} \i …