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...

dissertation, Gorenstein introduced a duality principle for plane curves that motivated Alexander Grothendieck's introduction of Gorenstein rings. Gorenstein held...

catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings A local complete intersection ring is a Noetherian...

rings, there is the following chain of inclusions. Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings...

theorem Gorenstein–Harada theorem Gorenstein ring Gorenstein scheme Gorenstein–Walter theorem Eli Gorenstein (born 1952), Israeli actor, voice actor...

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...

rings. For Noetherian local rings, there is the following chain of inclusions: Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃...

inclusions. Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings Suppose that A is a Noetherian...

Flat map Flat map (ring theory) Projective module Injective module Cohen-Macaulay ring Gorenstein ring Complete intersection ring Koszul complex Hilbert's...

ring Cohen–Macaulay ring Gorenstein ring Artinian ring, Noetherian ring Perfect ring, semiperfect ring Baer ring, Rickart ring Lie ring, Lie algebra Ideal...

(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...

by conditions about Gorenstein rings. Acceptable rings were introduced by Sharp (1977). All finite-dimensional Gorenstein rings are acceptable, as are...

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 ,...

Krull dimension Regular local ring Regular sequence Cohen–Macaulay ring Gorenstein ring Koszul complex Spectrum of a ring Zariski topology Kähler differential...

Petersen, Dan; Tommasi, Orsola (2012). "The Gorenstein conjecture fails for the tautological ring of $\mathcal{\bar M}_{2,n}$". Inventiones mathematicae...

Excellent ring Fibred category – Concept in category theory Formally smooth map Fundamental groupoid Fundamental group scheme Gorenstein ring – Local ring in...

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...

Compact space, Connected ring, Differential calculus over commutative algebras, Banach–Stone theorem Local rings: Gorenstein local ring (also used in Wiles's...

so simple. (More precisely, it can, but at the cost of imposing the Gorenstein ring condition.) In a characteristic turn, Grothendieck reformulated general...

a Gorenstein scheme is a locally Noetherian scheme whose local rings are all Gorenstein. The canonical line bundle is defined for any Gorenstein scheme...

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...

Mathematical Monographs, Cambridge University Press, ISBN 978-1275570412 Gorenstein ring Baker, H. F. (1938). "Francis Sowerby Macaulay. 1862-1937". Obituary...

zero-dimensional local Gorenstein rings containing their residue field and finite-dimensional over it. Frobenius algebras are quasi-Frobenius rings, and in particular...

construct the dualizing sheaf on X. coherent duality reflexive sheaf Gorenstein ring Dualizing module Hartshorne 1977, Ch. III, § 7. Kollár & Mori 1998...

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...

curve over an algebraically closed field, all of whose local rings are Gorenstein rings, the same statement as above holds, provided that the geometric...

{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...

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...

theory of modules over Noetherian rings, local cohomology, symbolic powers of ideals, Cohen-Macaulay rings, Gorenstein rings and Hilbert-Kunz functions. He...

normal complete Gorenstein algebraic spaces). A fundamental theorem of Birkar–Cascini–Hacon–McKernan from 2006 is that the canonical ring of a smooth or...