Questions about commutative rings, their ideals, and their modules.

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Computing generators of the positive component of a graded ring

Let $R$ be a sub-algebra of $\mathbb{Q}[X_1^{\pm 1}, \dots, X_n^{\pm 1}]$ given by finitely many generators, and let $\lambda$ be a linear form $\lambda : \mathbb{Z}^n \to \mathbb{Z}$. This defines a ...
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Recovering free modules from their projective limit

Let $\dotsc A_2 \to A_1 \to A_0$ be a sequence of surjective homomorphisms of commutative rings. Consider the projective limit $\varprojlim_i A_i$. If $S$ is an (infinite) set, then $\varprojlim_i ...