Journal ArticleDOI
Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
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This article is published in American Journal of Mathematics.The article was published on 1977-06-01. It has received 671 citations till now. The article focuses on the topics: Free algebra & Codimension.read more
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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
Hilbert functions of graded algebras
TL;DR: In this article, the additive group of R has a direct-sum decomposition R = R + R, +..., where RiRi C R,+j and 1 E R,.
Journal ArticleDOI
Extremal transitions and five-dimensional supersymmetric field theories
David R. Morrison,Nathan Seiberg +1 more
TL;DR: In this paper, the authors study five-dimensional supersymmetric field theories with one-dimensional Coulomb branch and find two new theories: E1 with U(1) symmetry and E0 with no symmetry, the latter is a non-trivial theory with no relevant operators preserving the super-Poincare symmetry.
Book
The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry
TL;DR: Free Resolutions and Hilbert Functions: Free resolutions and Hilbert functions have been studied in algebra and geometry as discussed by the authors, where free resolutions have been used to solve local cohomology problems.
Book ChapterDOI
Infinite Free Resolutions
TL;DR: The notes for a series of five lectures to the Barcelona Summer School in Commutative Algebra at the Centre de Recerca Matematica, Institut d'Estudis Catalans, July 15-26, 1996.