Book ChapterDOI
Projective Modules Over Polynomial Rings
S. M. Bhatwadekar
- pp 41-62
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TLDR
In this paper, Quillen [Q] and Suslin [Su 1] proved that every finitely generated projective module over a polynomial ring k[T 1,..., T n ] over a field k is free.Abstract:
In 1976, Quillen [Q] and Suslin [Su 1] proved the following conjecture of Serre:-Conjecture: (Serre) Every finitely generated projective module over a polynomial ring k[T 1,..., T n ] over a field k is free.read more
Citations
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Book
A1-Algebraic Topology over a Field
TL;DR: A 1-invariant sheaf as discussed by the authors is a strongly A 1-homology sheaf with the affine B.G. property for the linear groups and the Grassmanian.
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A Tutorial on GrÖbner Bases With Applications in Signals and Systems
Zhiping Lin,L. Xu,N.K. Bose +2 more
TL;DR: A reasonably detailed review is given of several fundamental theoretical issues that occur in the use of Grobner bases in multidimensional signals and systems applications, including the primeness of multivariate polynomial matrices, multivariate unimodularPolynomial matrix completion, and prime factorization of multidity matrices.
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Homotopy invariance of non-stable K1-functors
TL;DR: In this article, the Whitehead group of reductive algebraic groups is shown to be injective for any regular k-algebra R with the fraction field K. If k is infinite perfect, one also deduces that K1G (R) → K 1G (K) is injective.
Journal ArticleDOI
An introduction to constructive algebraic analysis and its applications
TL;DR: The main purpose of these lectures was to introduce the French community of symbolic computation to the constructive approach to algebraic analysis and particularly algebraic D-modules, its applications to mathematical systems theory and its implementations in computer algebra systems such as Maple or GAP4 as mentioned in this paper.
Journal ArticleDOI
The $G$-stable pieces of the wonderful compactification
TL;DR: In this paper, it was shown that the closure of any G-stable piece is a disjoint union of some Gstable pieces, which was first conjectured by Lusztig, and the existence of cellular decomposition if the closure contains finitely many -orbits.
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:
Book
Commutative Ring Theory
Hideyuki Matsumura,Miles Reid +1 more
TL;DR: In this article, the authors introduce the notion of complete local rings and apply it to a wide range of applications, including: I-smoothness, I-flatness revisited, and valuation rings.
Journal ArticleDOI
$K$-theory and stable algebra
TL;DR: In this article, the authors present a legal opinion on the use of commercial or impression systématiques in the context of the IHES agreement with the conditions générales d'utilisation.