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Topic · Algebra and Number Theory

Commutative Algebra and Its Applications

Commutative Algebra and Its Applications is a research topic within Algebra and Number Theory. Science Explorer counts 10k research works in it since 1950. 10.1% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the algebraic properties of monomial ideals, including their graded Betti numbers, local cohomology modules, symbolic powers, edge ideals, Cohen-Macaulay modules, Stanley depth, toric algebra, regularity bounds, and their connections to combinatorial topology.

  • Monomial Ideals
  • Graded Betti Numbers
  • Local Cohomology Modules
  • Symbolic Powers
  • Edge Ideals
  • Cohen-Macaulay Modules
  • Stanley Depth
  • Toric Algebra
  • Regularity Bounds
  • Combinatorial Topology
Research works
10k
fractional, since 1950
In the world top 10%
1k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+13%
the tick is no change
Largest producer
United States
27% of the 10 largest, 2022-now
Commutative Algebra and Its Applications

Which countries lead Commutative Algebra and Its Applications research?

By volume, the United States and China publish the most (300 and 149 works in 2022-now).

By volume, 2022-now

  1. 1 United States 300 works
  2. 2 China 149 works
  3. 3 India 139 works
  4. 4 Japan 99 works
  5. 5 Iran 84 works
  6. 6 Italy 81 works
  7. 7 Germany 76 works
  8. 8 France 67 works
  9. 9 Spain 54 works
  10. 10 Türkiye 50 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

United States: 27.3%China: 13.5%India: 12.6%Japan: 9.0%6 others listed: 37.5%27%largest
United States300 · 27.3%China149 · 13.5%India139 · 12.6%Japan99 · 9.0%6 others listed412 · 37.5%

Shares of the rows listed above, not of the whole node.

Which institutions lead Commutative Algebra and Its Applications research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Commutative Algebra and Its Applications research, followed by Chennai Mathematical Institute and Indian Institute of Technology Bombay.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 33 works
  2. 2 Chennai Mathematical InstituteIndia 13 works
  3. 3 Indian Institute of Technology BombayIndia 13 works
  4. 4 The University of OsakaJapan 11 works
  5. 5 University of MessinaItaly 11 works
  6. 6 Sidi Mohamed Ben Abdellah UniversityMorocco 10 works
  7. 7 Indian Institute of Technology KharagpurIndia 9 works
  8. 8 Max Planck SocietyGermany 9 works
  9. 9 Purdue University West LafayetteUnited States 9 works
  10. 10 Vietnam Academy of Science and TechnologyVietnam 9 works

Who are the leading researchers in Commutative Algebra and Its Applications?

The most-cited researchers publishing on Commutative Algebra and Its Applications include D. Craig Miller and Seth Lloyd.

  1. 1 D. Craig Miller United States 77k citations
  2. 2 Seth Lloyd United States 71k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Commutative Algebra and Its Applications?

The most cited paper in Commutative Algebra and Its Applications is "Hopf Algebras and Their Actions on Rings" (Susan Montgomery, 1993), with 2,592 citations. Next come "Computing Persistent Homology" (1,651) and "On Lovász’ lattice reduction and the nearest lattice point problem" (955).

Most cited papers
#PaperReleasedCitations
1 Hopf Algebras and Their Actions on Rings Susan Montgomery · Regional conference series in mathematics Conference paper 28 Oct 1993 2,592
2 Computing Persistent Homology Afra Zomorodian, Gunnar Carlsson · Discrete & Computational Geometry Open access 19 Nov 2004 1,651
3 On Lovász’ lattice reduction and the nearest lattice point problem László Babai · COMBINATORICA Mar 1986 955
4 Hilbert functions of graded algebras Richard P. Stanley · Advances in Mathematics Open access Apr 1978 898
5 On the ubiquity of Gorenstein rings Hyman E. Bass · Mathematische Zeitschrift 1963 896
All 100 most cited papers, with filters and sorting

Where is Commutative Algebra and Its Applications research done?

The largest centres of Commutative Algebra and Its Applications research in 2022-now are Tehran (Iran), Tokyo (Japan), Paris (France) and Beijing (China).

Largest cities, 2022-now

  1. 1 TehranIran 29 works
  2. 2 TokyoJapan 27 works
  3. 3 ParisFrance 26 works
  4. 4 BeijingChina 23 works
  5. 5 MoscowRussia 22 works
  6. 6 ChennaiIndia 18 works
  7. 7 HanoiVietnam 18 works
  8. 8 MumbaiIndia 16 works
  9. 9 OsakaJapan 15 works
  10. 10 BarcelonaSpain 13 works
See Commutative Algebra and Its Applications on the map

Where is the best place to study Commutative Algebra and Its Applications?

Among universities, judged by research, University of Messina, Chennai Mathematical Institute and Indian Institute of Technology Kharagpur score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 15.35%fractional works in this field (log) →share of work in the world top 10% →University of MessinaIndian Institute of …The University of Os…Chennai Mathematical…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1University of MessinaItaly 82.332.7%31.9×10 +202.5%
2Chennai Mathematical InstituteIndia 71.313.2%164.8×13 +178.6%
3Indian Institute of Technology KharagpurIndia 63.823.2%13.3×9 +238.5%
4The University of OsakaJapan 58.613.7%12.2×10 +6.5%
5Purdue University West LafayetteUnited States 54.717.6%6.8×9 +43.3%
6Indian Institute of Technology BombayIndia 50.02.2%20.9×13 +88.1%
7Sidi Mohamed Ben Abdellah UniversityMorocco 48.710.3%25.1×10 +39.9%
8University of UtahUnited States 45.614.2%8.7×8 +47.2%
9Universitat de BarcelonaSpain 45.014.3%7.7×8 +52.3%
10University of GenoaItaly 43.612.1%18.5×8 -0.5%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Commutative Algebra and Its Applications, country by country

Is Commutative Algebra and Its Applications research growing?

Output in 2022-2025 was 13% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Commutative Algebra and Its Applications.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Commutative Algebra and Its Applications as a percentage of every work published that year, 0.0062% in 2024.

still counting0.010%0.020%Commutative Algebra and Its Applications0.0063% in 202519801990200020102020

Fractional works of Commutative Algebra and Its Applications over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Commutative Algebra and Its Applications10.0% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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