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- Melvin Hochster

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
34
Citations
7,785
92
World Ranking
1977
National Ranking
845

1992 - Fellow of the American Academy of Arts and Sciences

1992 - Member of the National Academy of Sciences

1981 - Fellow of John Simon Guggenheim Memorial Foundation

1980 - Frank Nelson Cole Prize in Algebra

- Algebra
- Pure mathematics
- Topology

The scientist’s investigation covers issues in Discrete mathematics, Pure mathematics, Tight closure, Combinatorics and Algebra. Much of his study explores Discrete mathematics relationship to Prime characteristic. His Pure mathematics research includes elements of Von Neumann regular ring, Ring, Noetherian and Ideal.

His research investigates the connection between Tight closure and topics such as Regular ring that intersect with issues in Base change. His Combinatorics study combines topics from a wide range of disciplines, such as Cup product, De Rham cohomology, Cohomology and Graded ring. His Local ring study combines topics in areas such as Commutative algebra and Noncommutative ring.

- Prime ideal structure in commutative rings (547 citations)
- Tight closure, invariant theory, and the Briançon-Skoda theorem (537 citations)
- Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes (477 citations)

His primary scientific interests are in Pure mathematics, Discrete mathematics, Combinatorics, Ideal and Local ring. His study in Pure mathematics is interdisciplinary in nature, drawing from both Von Neumann regular ring, Commutative ring and Local cohomology. While the research belongs to areas of Local cohomology, Melvin Hochster spends his time largely on the problem of Group cohomology, intersecting his research to questions surrounding Čech cohomology, De Rham cohomology, Graded ring and Cup product.

He is involved in the study of Discrete mathematics that focuses on Zariski topology in particular. His Combinatorics research includes themes of Subring and Field. His Ideal study integrates concerns from other disciplines, such as Ring, Noetherian, Polynomial ring and Domain.

- Pure mathematics (52.48%)
- Discrete mathematics (34.65%)
- Combinatorics (25.74%)

- Pure mathematics (52.48%)
- Combinatorics (25.74%)
- Polynomial ring (17.82%)

Pure mathematics, Combinatorics, Polynomial ring, Ideal and Local cohomology are his primary areas of study. In the field of Pure mathematics, his study on Conjecture overlaps with subjects such as In degree. His Combinatorics research incorporates themes from Field and Algebra.

His Polynomial ring research integrates issues from Regular sequence and Degree. His research integrates issues of Characterization, Discrete mathematics and Tight closure in his study of Local cohomology. His Dimension research is multidisciplinary, relying on both Noetherian, Image and Local ring.

- Small Subalgebras of Polynomial Rings and Stillman's Conjecture (20 citations)
- Small subalgebras of polynomial rings and Stillman’s Conjecture (17 citations)
- Homological Conjectures and Lim Cohen-Macaulay Sequences (8 citations)

- Algebra
- Pure mathematics
- Topology

Melvin Hochster mainly focuses on Pure mathematics, Local cohomology, Ring, Polynomial ring and Ideal. His studies deal with areas such as Ring theory and Sequence as well as Pure mathematics. His research in Local cohomology intersects with topics in Discrete mathematics, Tight closure and Perfectoid.

The various areas that Melvin Hochster examines in his Ring study include Degree, Algebraically closed field, Regular sequence, Combinatorics and Bounded function. His work carried out in the field of Combinatorics brings together such families of science as Noetherian, Image and Maximal ideal. As part of his studies on Polynomial ring, Melvin Hochster frequently links adjacent subjects like Primary decomposition.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Prime ideal structure in commutative rings

Melvin Hochster.

Transactions of the American Mathematical Society **(1969)**

888 Citations

Prime ideal structure in commutative rings

Melvin Hochster.

Transactions of the American Mathematical Society **(1969)**

888 Citations

Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes

M. Hochster.

Annals of Mathematics **(1972)**

752 Citations

Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes

M. Hochster.

Annals of Mathematics **(1972)**

752 Citations

Tight closure, invariant theory, and the Briançon-Skoda theorem

Melvin Hochster;Craig Huneke;Craig Huneke.

Journal of the American Mathematical Society **(1990)**

634 Citations

Tight closure, invariant theory, and the Briançon-Skoda theorem

Melvin Hochster;Craig Huneke;Craig Huneke.

Journal of the American Mathematical Society **(1990)**

634 Citations

Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci

M. Hochster;John A. Eagon.

American Journal of Mathematics **(1971)**

579 Citations

Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci

M. Hochster;John A. Eagon.

American Journal of Mathematics **(1971)**

579 Citations

Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay

Melvin Hochster;Joel L Roberts.

Advances in Mathematics **(1974)**

560 Citations

Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay

Melvin Hochster;Joel L Roberts.

Advances in Mathematics **(1974)**

560 Citations

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