In commutative algebra, a Gorenstein local ring is a commutative Noetherian local ring R with finite injective dimension as an R-module. There are many...
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dissertation, Gorenstein introduced a duality principle for plane curves that motivated Alexander Grothendieck's introduction of Gorenstein rings. Gorenstein held...
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catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings A local complete intersection ring is a Noetherian...
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rings, there is the following chain of inclusions. Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings...
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theorem Gorenstein–Harada theorem Gorenstein ring Gorenstein scheme Gorenstein–Walter theorem Eli Gorenstein (born 1952), Israeli actor, voice actor...
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Artin algebra Artinian ideal Serial module Semiperfect ring Gorenstein ring Noetherian ring Brešar 2014, p. 73 Clark, Theorem 20.11 Cohn 2003, 5.2 Exercise...
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rings. For Noetherian local rings, there is the following chain of inclusions: Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃...
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inclusions. Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings Suppose that A is a Noetherian...
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Flat map Flat map (ring theory) Projective module Injective module Cohen-Macaulay ring Gorenstein ring Complete intersection ring Koszul complex Hilbert's...
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List of abstract algebra topics (section Ring theory)
ring Cohen–Macaulay ring Gorenstein ring Artinian ring, Noetherian ring Perfect ring, semiperfect ring Baer ring, Rickart ring Lie ring, Lie algebra Ideal...
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(2nd ed.). Dover. ISBN 978-0-486-47187-7. Discrete valuation ring Semi-local ring Valuation ring Gorenstein local ring The philosophy behind local rings...
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by conditions about Gorenstein rings. Acceptable rings were introduced by Sharp (1977). All finite-dimensional Gorenstein rings are acceptable, as are...
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Injective module (redirect from Self-injective ring)
every local Gorenstein ring which is also Artin is injective over itself since has a 1-dimensional socle. A simple non-example is the ring R = C [ x ,...
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Glossary of commutative algebra (redirect from Glossary of commutative ring theory)
about Gorenstein rings. adic The I-adic topology on a ring has a base of neighborhoods of 0 given by powers of the ideal I. affine ring An affine ring R over...
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Krull dimension Regular local ring Regular sequence Cohen–Macaulay ring Gorenstein ring Koszul complex Spectrum of a ring Zariski topology Kähler differential...
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Petersen, Dan; Tommasi, Orsola (2012). "The Gorenstein conjecture fails for the tautological ring of $\mathcal{\bar M}_{2,n}$". Inventiones mathematicae...
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Excellent ring Fibred category – Concept in category theory Formally smooth map Fundamental groupoid Fundamental group scheme Gorenstein ring – Local ring in...
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Compact space, Connected ring, Differential calculus over commutative algebras, Banach–Stone theorem Local rings: Gorenstein local ring (also used in Wiles's...
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so simple. (More precisely, it can, but at the cost of imposing the Gorenstein ring condition.) In a characteristic turn, Grothendieck reformulated general...
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a Gorenstein scheme is a locally Noetherian scheme whose local rings are all Gorenstein. The canonical line bundle is defined for any Gorenstein scheme...
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Cohen–Macaulay ring is a quotient of a Gorenstein ring then it has a dualizing module. In particular any complete local Cohen–Macaulay ring has a dualizing...
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Mathematical Monographs, Cambridge University Press, ISBN 978-1275570412 Gorenstein ring Baker, H. F. (1938). "Francis Sowerby Macaulay. 1862-1937". Obituary...
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Frobenius algebra (redirect from Frobenius ring)
zero-dimensional local Gorenstein rings containing their residue field and finite-dimensional over it. Frobenius algebras are quasi-Frobenius rings, and in particular...
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construct the dualizing sheaf on X. coherent duality reflexive sheaf Gorenstein ring Dualizing module Hartshorne 1977, Ch. III, § 7. Kollár & Mori 1998...
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results on subgroups of GL2(k) Chapter 2 479 1. The Gorenstein property 489 2. Congruences between Hecke rings 503 3. The main conjectures Chapter 3 517 Estimates...
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curve over an algebraically closed field, all of whose local rings are Gorenstein rings, the same statement as above holds, provided that the geometric...
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Glossary of algebraic geometry (redirect from Section ring)
{O}}_{X})^{G}={\mathcal {O}}_{Y}.} Gorenstein 1. A Gorenstein scheme is a locally Noetherian scheme whose local rings are Gorenstein rings. 2. A normal variety is...
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Perfect ideal (category Ideals (ring theory))
David; Gray, Jeremy (2023). "F. S. Macaulay: From plane curves to Gorenstein rings". Bull. Amer. Math. Soc. 60 (3): 371–406. doi:10.1090/bull/1787. Retrieved...
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Canonical bundle (section Canonical rings)
normal complete Gorenstein algebraic spaces). A fundamental theorem of Birkar–Cascini–Hacon–McKernan from 2006 is that the canonical ring of a smooth or...
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theory of modules over Noetherian rings, local cohomology, symbolic powers of ideals, Cohen-Macaulay rings, Gorenstein rings and Hilbert-Kunz functions. He...
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