Melvin Hochster

Q: What Schools Are Affiliated With Melvin Hochster

Melvin Hochster is affiliated with the following schools: University of Minnesota, University of Michigan, Princeton University, Purdue University, Harvard University

Melvin Hochster's AcademicInfluence.com Rankings

Melvin Hochster

Mathematics

#773

World Rank

#1398

Historical Rank

#338

USA Rank

Measure Theory

#1617

World Rank

#1996

Historical Rank

#535

USA Rank

mathematics Degrees

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Mathematics

Why Is Melvin Hochster Influential?

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According to Wikipedia, Melvin Hochster is an American mathematician working in commutative algebra. He is currently the Jack E. McLaughlin Distinguished University Professor Emeritus of Mathematics at the University of Michigan.

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Melvin Hochster's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Prime ideal structure in commutative rings (1969) (669)
Tight closure, invariant theory, and the Briançon-Skoda theorem (1990) (564)
Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes (1972) (526)
Invariant theory and the generic perfection of determinantal loci (1971) (433)
Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay (1974) (423)
$F$-regularity, test elements, and smooth base change (1994) (303)
Topics in the Homological Theory of Modules over Commutative Rings (1975) (258)
Comparison of symbolic and ordinary powers of ideals (2002) (243)
The purity of the Frobenius and local cohomology (1976) (226)
Tight closure and strong F-regularity (1989) (180)
Infinite integral extensions and big Cohen-Macaulay algebras (1992) (139)
Canonical elements in local cohomology modules and the direct summand conjecture (1983) (137)
Cyclic purity versus purity in excellent Noetherian rings (1977) (124)
Criteria for equality of ordinary and symbolic powers of primes (1973) (108)
Applications of the Existence of Big Cohen-Macaulay Algebras (1995) (106)
A Nullstellensatz with nilpotents and Zariski's Main Lemma on holomorphic functions (1979) (95)
INDECOMPOSABLE CANONICAL MODULES AND CONNECTEDNESS (2002) (91)
Cohen-macaulay modules (1973) (90)
^-REGULARITY, TEST ELEMENTS, AND SMOOTH BASE CHANGE (2010) (76)
Five theorems on Macaulay rings (1973) (67)
Grassmannians and their Schubert subvarieties are arithmetically Cohen-Macaulay (1973) (67)
Modules of finite projective dimension with negative intersection multiplicities (1985) (67)
Big Cohen–Macaulay algebras in dimension three via Heitmann's theorem (2002) (62)
The Frobenius structure of local cohomology (2007) (62)
Small subalgebras of polynomial rings and Stillman’s Conjecture (2016) (61)
Nonuniqueness of coefficient rings in a polynomial ring (1972) (61)
Properties of Noetherian rings stable under general grade reduction (1973) (58)
Tight closure and elements of small order in integral extensions (1991) (47)
R-SEQUENCES AND INDETERMINATES (1974) (46)
The Minimal Prime Spectrum of a Commutative Ring (1971) (42)
THE NOTION OF TIGHT CLOSURE IN EQUAL CHARACTERISTIC ZERO (2014) (42)
Localization and test exponents for tight closure. (2002) (40)
The Zariski-Lipman conjecture in the graded case (1977) (39)
Homological conjectures, old and new (2007) (37)
Grade-Sensitive Modules and Perfect Modules (1974) (35)
Non-openness of loci in Noetherian rings (1973) (34)
The dimension of an intersection in an ambient hypersurface (1981) (33)
Some applications of the Frobenius in characteristic 0 (1978) (30)
Tightly closed ideals (1988) (29)
Fine behavior of symbolic powers of ideals (2007) (28)
Ideals Generated by Quadratic Polynomials (2011) (26)
Totally integrally closed rings and extremal spaces (1970) (25)
Subsemigroups of amenable groups (1969) (25)
Homological invariants of modules over contracting endomorphisms (2010) (21)
A class of perfect determinantal ideals (1970) (21)
Finite Tor dimension and failure of coherence in absolute integral closures (1997) (20)
Absolute integral closures are big Cohen-Macaulay algebras in characteristic $P$ (1991) (19)
Homological Conjectures and Lim Cohen-Macaulay Sequences (2017) (18)
The equicharacteristic case of some homological conjectures on local rings (1974) (17)
Euler characteristics over unramified regular local rings (1984) (16)
Continuous closure, axes closure, and natural closure (2011) (15)
Strength conditions, small subalgebras, and Stillman bounds in degree ≤4 (2018) (15)
Generically Perfect Modules are Strongly Generically Perfect (1971) (14)
Presentation depth and the Lipman-Sathaye Jacobian theorem (2002) (13)
Big and small Cohen-Macaulay modules (1979) (11)
Actions of reductive groups on regular rings and Cohen-Macaulay rings (1974) (11)
Support of local cohomology modules over hypersurfaces and rings with FFRT (2017) (11)
Tight Closure Theory and Characteristic p Methods (2005) (11)
Symbolic powers in Noetherian domains (1971) (11)
An obstruction to lifting cyclic modules (1975) (11)
Deep local rings (1973) (10)
Expanded radical ideals and semiregular ideals (1973) (8)
The Tight Integral Closure of a Set of Ideals (2000) (8)
The Zariski-Lipman conjecture for homogeneous complete intersections (1975) (8)
Splitting theorems for quadratic ring extensions (1983) (8)
Finiteness properties and numerical behavior of local cohomology (2019) (8)
The F-rational signature and drops in the Hilbert–Kunz multiplicity (2022) (7)
The Eisenbud–Green–Harris conjecture for defect two quadratic ideals (2018) (7)
Current state of the homological conjectures : Five talks of a (2004) (7)
Quasilength, latent regular sequences, and content of local cohomology (2009) (6)
Content of local cohomology, parameter ideals, and robust algebras (2016) (6)
Existence of topologies for commutative rings with identity (1971) (6)
Extensions of primes, flatness, and intersection flatness (2020) (5)
Rings with nondiscrete ideal topologies (1969) (5)
A Jacobian criterion for nonsingularity in mixed characteristic (2021) (5)
Faithfulness of top local cohomology modules in domains (2019) (5)
Commutative algebra : proceedings of a microprogram held June 15-July 2, 1987 (1989) (4)
Commutative Algebra: The local homological conjectures (1983) (3)
F-Purity, Frobenius Splitting, and Tight Closure (2013) (2)
TIGHT CLOSURE IN EQUAL CHARACTERISTIC (2014) (2)
Book Review: Cohen-Macaulay rings (1995) (2)
Rings of continuous functions and totally integrally closed rings (1970) (2)
Commutative rings with identity have ring topologies (1970) (2)
Test exponents for modules with finite phantom projective dimension (2012) (2)
Principal ideal theorems (1979) (1)
Cohen-Macaulay varieties, geometric complexes, and combinatorics (2016) (1)
When are the natural embeddings of classical invariant rings pure? (2022) (1)
[Preliminary Version] AN EMBEDDING THEOREM FOR MODULES OF FINITE (G-)PROJECTIVE DIMENSION (2009) (1)
Lower bounds for Betti numbers of special extensions (2005) (1)
Pathological maximal R-sequences in quasilocal domains (1979) (1)
Applications of Algebraic Geometry to Combinatorics (Commutative Algebra and Algebraic Geometry) (1981) (0)
Universal lex ideal approximations of extended Hilbert functions and Hamilton numbers (2020) (0)
Some Open Questions (1975) (0)
Tight closure and strongly F-regular rings (2022) (0)
Henselian Rings, M. Artin’s Approximation Theorem, and Big Cohen-Macaulay Modules Over Fields of Characteristic 0 (1975) (0)
Shorter Notes: The Zariski-Lipman Conjecture for Homogeneous Complete Intersections (1975) (0)
Review: D. G. Northcott, Finite free resolutions (1978) (0)
Corrigendum to “Strength conditions, small subalgebras, and Stillman bounds in degree $\leq 4$” (2020) (0)
Modules of Projective Dimension 2, Generic Modules of Finite Projective Dimension, and the Buchsbaum-Eisenbud Structure Theorems (1975) (0)
CYCLIC PURITY VERSUS PURITY IN EXCELLENT (2010) (0)
Depth-Sensitivity Theorems and Exactness Criteria (1975) (0)
THE DIRECT SUM DECOMPOSABILITY OF M IN DIMENSION TWO (2008) (0)
The mathematical contributions of Craig Huneke (2021) (0)
Comment on “Resistance Circuits and Things Synthesized by Number Theory” (1961) (0)
Advanced Problems: 6296-6299 (1980) (0)
Modifications and the Existence of Big Cohen-Macaulay Modules in Characteristic >0 (1975) (0)
Consequences of the Existence of Cohen-Macaulay Modules (1975) (0)
Tight closure and strongly F-regular rings (2022) (0)
D-MODULES AND LYUBEZNIK’S FINITENESS THEOREMS FOR LOCAL COHOMOLOGY (2011) (0)
Applications of Homological Methods and Some More Open Questions (1975) (0)
Homological invariants of modules over contracting endomorphisms (2011) (0)
Special issue celebrating the 60th birthday of Paul Roberts (2009) (0)
Remembering David Buchsbaum (2022) (0)
Local cohomology with support in a parameter ideal (2013) (0)
Book Review: Multiplicities and Chern classes in local algebra (2000) (0)
Commutative Noetherian local rings (1979) (0)
Linear Algebraic Groups (1975) (0)

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What Schools Are Affiliated With Melvin Hochster?

Melvin Hochster is affiliated with the following schools:

Melvin Hochster's Academic­Influence.com Rankings