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Topic · Algebra and Number Theory

Rings, Modules, and Algebras

Rings, Modules, and Algebras is a research topic within Algebra and Number Theory. Science Explorer counts 21k research works in it since 1950. 9.4% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the study of properties and structures of commutative rings, including topics such as zero-divisor graphs, Armendariz rings, idealization, Baer rings, nil-clean rings, annihilator ideals, quasi-Baer rings, factorization theory, triangular matrix representations, and semistar operations.

  • Zero-Divisor Graphs
  • Armendariz Rings
  • Idealization
  • Baer Rings
  • Nil-Clean Rings
  • Annihilator Ideals
  • Quasi-Baer Rings
  • Factorization Theory
  • Triangular Matrix Representations
  • Semistar Operations
Research works
21k
fractional, since 1950
In the world top 10%
2k
per year above
Top-10% rate
9.4%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+10%
the tick is no change

Which countries lead Rings, Modules, and Algebras research?

By volume, India and China publish the most (295 and 238 works in 2022–2025).

By volume, 2022–2025

  1. 1 India 295 works
  2. 2 China 238 works
  3. 3 United States 228 works
  4. 4 Iraq 175 works
  5. 5 Iran 169 works
  6. 6 Türkiye 140 works
  7. 7 Russia 95 works
  8. 8 Italy 75 works
  9. 9 Morocco 68 works
  10. 10 Japan 64 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.

India: 19.1%China: 15.4%United States: 14.8%Iraq: 11.3%6 others listed: 39.5%19%largest
India295 · 19.1%China238 · 15.4%United States228 · 14.8%Iraq175 · 11.3%6 others listed612 · 39.5%

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

Which institutions lead Rings, Modules, and Algebras research?

By volume in 2022–2025, University of Baghdad publishes the most Rings, Modules, and Algebras research, followed by Sidi Mohamed Ben Abdellah University and Aligarh Muslim University.

By volume, 2022–2025

  1. 1 University of BaghdadIraq 43 works
  2. 2 Sidi Mohamed Ben Abdellah UniversityMorocco 34 works
  3. 3 Aligarh Muslim UniversityIndia 30 works
  4. 4 University of TikritIraq 21 works
  5. 5 Lomonosov Moscow State UniversityRussia 18 works
  6. 6 University of MosulIraq 17 works
  7. 7 University of Al-QadisiyahIraq 14 works
  8. 8 University of DelhiIndia 13 works
  9. 9 Jadavpur UniversityIndia 12 works
  10. 10 University of MonastirTunisia 12 works

Who are the leading researchers in Rings, Modules, and Algebras?

The most-cited researchers publishing on Rings, Modules, and Algebras include Jeremy C. Smith, Gian‐Carlo Rota and David J. Benson.

  1. 1 Jeremy C. Smith United States 2.3k citations
  2. 2 Gian‐Carlo Rota United States 1.8k citations
  3. 3 David J. Benson United States 1.5k citations

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

Where is Rings, Modules, and Algebras research done?

The largest centres of Rings, Modules, and Algebras research in 2022–2025 are Baghdad (Iraq), Tehran (Iran), Moscow (Russia) and Fes (Morocco). Among places with at least 20 works in it, it is an unusually large share of all research in Fes, Aligarh and Tikrit.

Largest cities, 2022–2025

  1. 1 Baghdad Iraq 63 works
  2. 2 Tehran Iran 51 works
  3. 3 Moscow Russia 43 works
  4. 4 Fes Morocco 34 works
  5. 5 Aligarh India 30 works
  6. 6 Beijing China 25 works
  7. 7 Paris France 23 works
  8. 8 Nanjing China 23 works
  9. 9 Kolkata India 22 works
  10. 10 Tikrit Iraq 21 works

Where it is the local speciality

  1. FesMA · 34.3 works39×
  2. AligarhIN · 29.5 works38×
  3. TikritIQ · 21.2 works32×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Rings, Modules, and Algebras than the world average.

See Rings, Modules, and Algebras on the map

Where is the best place to study Rings, Modules, and Algebras?

Among universities, judged by research, University of Baghdad, Cukurova University and Aligarh Muslim University 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 12.46%fractional works in this node (log) →share in the world top 10% →University of Baghdad: 42, 7.5%Cukurova University: 11, 36.5%Aligarh Muslim University: 30, 17.3%Sidi Mohamed Ben Abdellah University: 34, 4.6%University of Tikrit: 21, 4.7%Amasya Üniversitesi: 11, 13.3%University of Al-Qadisiyah: 14, 4.3%Manonmaniam Sundaranar University: 10, 9.0%Charles University: 10, 19.1%Lomonosov Moscow State University: 18, 8.3%Cukurova UniversityAligarh Muslim Unive…University of BaghdadSidi Mohamed Ben Abd…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 University of BaghdadIraq 67.17.5%24.3×42 +224.3%
2 Cukurova UniversityTürkiye 65.736.5%17.9×11 —
3 Aligarh Muslim UniversityIndia 63.417.3%44.9×30 +34.9%
4 Sidi Mohamed Ben Abdellah UniversityMorocco 58.94.6%51.2×34 +123.6%
5 University of TikritIraq 55.74.7%32.1×21 +222.2%
6 Amasya ÜniversitesiTürkiye 54.913.3%48.1×11 +325.0%
7 University of Al-QadisiyahIraq 52.14.3%38.1×14 +256.9%
8 Manonmaniam Sundaranar UniversityIndia 49.69.0%48.6×10 +174.1%
9 Charles UniversityCzechia 49.419.1%8.9×10 +9.0%
10 Lomonosov Moscow State UniversityRussia 48.18.3%8.6×18 +14.5%

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Rings, Modules, and Algebras research growing?

Output in 2018–2022 was 10% higher than in 2013–2017, peaking in 2025. The fastest-growing topics are Rings, Modules, and Algebras.

19801990200020102020
grewheldshrank

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

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.