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Commutative Algebra I
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A compilation of two sets of notes at the University of Kansas was published in the Spring of 2002 by?? and the other in the spring of 2007 by Branden Stone.Abstract:
1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typedread more
Citations
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Extension theorems for reductive group schemes
TL;DR: In this article, the existence of good integral models of Shimura varieties of Hodge type has been shown to be true for adjoint group schemes, and it is shown that every Lie algebra with a perfect Killing form over a commutative Z-algebra, is the Lie algebra of an adjoint GFG.
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A closer look at the approximation capabilities of neural networks
TL;DR: A direct algebraic proof of the universal approximation theorem is given and it is shown there exists some $N\in \mathcal{O}(\varepsilon^{-n})$ (independent of $m$), such that $N$ hidden units would suffice to approximate $f$.
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On the fattening of lines in P3
TL;DR: In this article, the authors follow the lead of [2] and show how differences in the invariant α can be used to classify certain classes of subschemes of P 3.
Singularities with Gm-Action and the log minimal model program for Mg
TL;DR: In this paper, the modularity principle for the log canonical models Mg(α) := Proj ⊕ d≥0 H (Mg, bd(KMg +αδ)c).
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Some Simple Derivations of k[x, y]
TL;DR: In this article, it was shown that the polynomial ring in two variables over a field k of characteristic zero is a simple derivation of k[x, y], where 0 ≤ r ≤ r < s are integers.
References
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Book
Introduction to Commutative Algebra
TL;DR: It is shown here how the Noetherian Rings and Dedekind Domains can be transformed into rings and Modules of Fractions using the following structures: