Open Problems on Syzygies and Hilbert Functions
Irena Peeva,Michael Stillman +1 more
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This article is published in Journal of Commutative Algebra.The article was published on 2009-03-01 and is currently open access. It has received 86 citations till now. The article focuses on the topics: Hilbert manifold & Hilbert's fourteenth problem.read more
Citations
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Edge Ideals: Algebraic and Combinatorial Properties
Susan Morey,Rafael H. Villarreal +1 more
TL;DR: A survey of algebraic and combinatorial properties of R/I(C) and C, respectively, can be found in this paper, where the authors give a criterion to estimate the regularity of the ideal of vertex covers of C. They also examine the associated primes of powers of edge ideals and show that these sets form an ascending chain.
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Small Subalgebras of Polynomial Rings and Stillman's Conjecture
Tigran Ananyan,Melvin Hochster +1 more
TL;DR: In this paper, it was shown that the projective dimension of a polynomial ring whose generators are forms of degree is bounded independent of the number of primary components and the number and number of generators of all the prime and primary ideals occurring.
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Topological Noetherianity of polynomial functors
TL;DR: In this paper, it was shown that any finite-degree polynomial functor over an infinite field is topologically Noetherian, which implies boundedness of a wider class of invariants of ideals.
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Small subalgebras of polynomial rings and Stillman’s Conjecture
Tigran Ananyan,Melvin Hochster +1 more
TL;DR: It is shown that in a polynomial ring of arbitrary characteristic, any .
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Big polynomial rings and Stillman’s conjecture
TL;DR: In this article, it was shown that certain limits of polynomial rings are themselves polynomials, and this observation can be used to deduce some interesting results in commutative algebra.
References
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Book
Combinatorics and commutative algebra
TL;DR: An overview of the connections between commutative algebra and combinatorics can be found in this article, where the authors present a survey of recent work related to face rings, focusing on applications to f-vectors.
Book
Arrangements of hyperplanes
Peter Orlik,Hiroaki Terao +1 more
TL;DR: In this paper, the authors introduce the notion of three-dimensional restrictions for three dimensions in algebraic topology, based on the Index of Symbols of Symbolic Symbols (IOS).
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Homological algebra on a complete intersection, with an application to group representations
TL;DR: In this article, it was shown that the maximal Cohen-Macaulay modules with periodic resolutions are the maximal 4-modules without free direct summands, and the maximal 5-modules with periodic resolution are maximal 3-modules.
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The complexity of the word problems for commutative semigroups and polynomial ideals
Ernst W. Mayr,Albert R. Meyer +1 more
TL;DR: In this paper, a simple decision procedure for the word problems for commutative semigroups and polynomial deals is presented, which requires computational storage space growing exponentially with the size of the problem instance to which the procedure is applied.
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Some Properties of Enumeration in the Theory of Modular Systems
TL;DR: In this paper, the limiting relations which must exist between the terms of the series Do, Dv..., A, ••• where A is the number of linearly independent homogeneous polynomials of degree I (or of degrees less than or equal to I in the case of non-homogeneous poynomials) belonging to some actual modular system, the system being either perfectly general or else general of its kind.