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Commutative Algebra: with a View Toward Algebraic Geometry
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In this article, the authors define basic constructions and dimension theory, and apply them to the problem of homological methods for combinatorial problem solving in the context of homology.Abstract:
Introduction.- Elementary Definitions.- I Basic Constructions.- II Dimension Theory.- III Homological Methods.- Appendices.- Hints and Solutions for Selected Exercises.- References.- Index of Notation.- Index.read more
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Complexity and Real Computation
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Combinatorial Commutative Algebra
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TL;DR: In this paper, the authors present a set of monomial ideals for three-dimensional staircases and cellular resolutions, including two-dimensional lattice ideals, and a threedimensional staircase with cellular resolutions.
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Solving systems of polynomial equations
TL;DR: Polynomials in one variable Grobner bases of zero-dimensional ideals Bernstein's theorem and fewnomials as mentioned in this paper are the primary decomposition of polynomial systems in economics and statistics.
References
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Methods of Homological Algebra
Sergei Gelfand,Yuri I. Manin +1 more
TL;DR: In this article, the authors introduce homotopic algebra and define the notion of simplicial sets, derived categories and derived functors, and triangulated categories for homotopy algebra.
Journal ArticleDOI
On the Periods of Certain Rational Integrals: II
TL;DR: In this paper, the authors re-prove Macaulay's theorem 4.11 is essentially equivalent to a suitable vanishing theorem for sheaf cohomology and give a proof of the de Rham algebraic theorem used in the proof of Theorem 5.3.
Journal ArticleDOI
On the Geometry of a Theorem of Riemann
TL;DR: In this paper, the tangent cone of a smooth complete algebraic curve is described at any point in a projective space representing a complete linear system of effective divisors on the curve.
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How Much Land Does a Man Need
TL;DR: Little Black Classics: 80 books for Penguin's 80th birthday Little Black Classics celebrate the huge range and diversity of Penguin Classics, with books from around the world and across many centuries They take us from a balloon ride over Victorian London to a garden of blossom in Japan, from Tierra del Fuego to 16th-century California and the Russian steppe as discussed by the authors.
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