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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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Various Differents for 0-Dimensional Schemes and Applications
TL;DR: In this paper, the Noether, Dedekind, and Kahler differents for a 0-dimensional scheme X in the projective n-space P^n_K over an arbitrary field K were investigated.
An Arakelov-theoretic approach to naïve heights on hyperelliptic Jacobians
TL;DR: In this article, the authors use Arakelov theory to define a height on divisors of degree zero on a hyperelliptic curve over a global field, and show that this height has computably bounded difference from the Neron-Tate height of the corresponding point on the Jacobian.
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Rigid Ideals in Gorenstein Rings of Dimension One
TL;DR: In this paper, the existence of ideals I in a one-dimensional Gorenstein local ring R satisfying the property that I,I,I = 0$672 is investigated.
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Dagger closure in regular rings containing a field
Holger Brenner,Axel Stäbler +1 more
TL;DR: In this article, it was shown that the full rank one closure coincides with tight closure in positive characteristic under mild finiteness conditions, and that the forcing algebra for an element contained in dagger closure is parasolid.
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Pure subrings of commutative rings
TL;DR: In this article, the authors study subalgebras of affine or local algesbras such that the affine subalgebraic extension of a local affine algebra is a pure extension from algebraic and geometric viewpoints.
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: