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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
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SOME REMARKS ON THE p-BASIS AND DIFFERENTIAL BASIS
TL;DR: In this article, the existence of difierential basis of a regular local ring R of character-istic p > 0 over R p is shown to be a p -basis of R over R P.
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A note on the FIP property for extensions of commutative rings
Nasr Ben Mabrouk,Nabil Zeidi +1 more
TL;DR: In this article, the primitive element theorem for ring extensions is generalized to ring extensions, and sufficient and necessary conditions are given for a ring extension to have or not to have FIP, where S = R with a nilpotent element of S.
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A constructive approach to one-dimensional Gorenstein -algebras
Joan Elias,Maria Evelina Rossi +1 more
TL;DR: In this paper, the authors give constructive and finite procedures for the construction of Artinian Gorenstein k-algebras of dimension one and any codimension, and show that these submodules in positive dimension are not finitely generated.
Posted Content
A Horrocks' theorem for reflexive sheaves
TL;DR: In this paper, the authors define $m$-tail reflexive sheaves as reflexive heaves on projective spaces with the simplest possible cohomology, and prove that the rank of any $m-tail-rewardive sheaf on the projective space is greater or equal to 1/n-m.
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On the $\mu$ equals zero conjecture for fine Selmer groups in Iwasawa theory
TL;DR: In this paper , the vanishing of the $\mu$-invariant conjecture is shown to follow from a natural property satisfied by Galois deformation rings, and conditions under which the conjecture holds for various Galois representations of interest.
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: