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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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Spanning Lattice Polytopes and the Uniform Position Principle
TL;DR: In this paper, it was shown that Bertini's theorem holds under much milder assumptions, namely if the lattice polytope $P$ is spanning, i.e., any lattice point of the ambient lattice is an integer affine combination of lattice points in $P$.
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Frobenius projective and affine geometry of varieties in positive characteristic
TL;DR: In this paper, a theory of Frobenius-projective and affine structures on higher-dimensional varieties in positive characteristic has been proposed, which has been previously investigated only in the case where the underlying varieties are curves.
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Local Darboux first integrals of analytic differential systems
TL;DR: In this article, local and formal Darboux first integrals of analytic differential systems were discussed using the theory of Poincare-Dulac normal forms, and the effect of local Darboubles integrability on analytic normalization was studied.
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Model theory of fields with free operators in positive characteristic
TL;DR: In this paper, the authors give algebraic conditions about a finite algebra over a perfect field of positive characteristic, which are equivalent to the companionability of the theory of fields with "$B$-operators" (i.e., the operators coming from homomorphisms into tensor products with $B$).
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An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms
TL;DR: In this paper, an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field is given, which is of Colombeau type and contains a copy of the space of Schwartz distributions.
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: