Science Explorer Back to mapMap
Discussion
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. 9.9% 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%
2.1k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+13%
the tick is no change
Largest producer
India
19% of the 10 largest, 2022-now
Rings, Modules, and Algebras

Which countries lead Rings, Modules, and Algebras research?

By volume, India and China publish the most (344 and 300 works in 2022-now).

By volume, 2022-now

  1. 1 India 344 works
  2. 2 China 300 works
  3. 3 United States 260 works
  4. 4 Iraq 191 works
  5. 5 Iran 180 works
  6. 6 Türkiye 156 works
  7. 7 Russia 107 works
  8. 8 Italy 85 works
  9. 9 Morocco 77 works
  10. 10 Germany 75 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: 19.4%China: 16.9%United States: 14.7%Iraq: 10.7%6 others listed: 38.3%19%largest
India344 · 19.4%China300 · 16.9%United States260 · 14.7%Iraq191 · 10.7%6 others listed680 · 38.3%

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

Which institutions lead Rings, Modules, and Algebras research?

By volume in 2022-now, 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-now

  1. 1 University of BaghdadIraq 49 works
  2. 2 Sidi Mohamed Ben Abdellah UniversityMorocco 37 works
  3. 3 Aligarh Muslim UniversityIndia 31 works
  4. 4 Centre National de la Recherche ScientifiqueFrance 31 works
  5. 5 Russian Academy of SciencesRussia 22 works
  6. 6 University of TikritIraq 22 works
  7. 7 Lomonosov Moscow State UniversityRussia 19 works
  8. 8 University of MosulIraq 19 works
  9. 9 Bulgarian Academy of SciencesBulgaria 15 works
  10. 10 University of Al-QadisiyahIraq 15 works

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

The most-cited researchers publishing on Rings, Modules, and Algebras include Stephen M. Smith, Jean Piaget and Muhammad Ashraf.

  1. 1 Stephen M. Smith United Kingdom 214k citations
  2. 2 Jean Piaget Switzerland 104k citations
  3. 3 Muhammad Ashraf Pakistan 96k 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 Rings, Modules, and Algebras?

The most cited paper in Rings, Modules, and Algebras is "Rings of Continuous Functions." (Edgar R. Lorch, Leonard Gillman, Meyer Jerison, 1961), with 2,342 citations. Next come "On Ideal Lattices and Learning with Errors over Rings" (1,835) and "The Zero-Divisor Graph of a Commutative Ring" (1,350).

Most cited papers
#PaperReleasedCitations
1 Rings of Continuous Functions. Edgar R. Lorch, Leonard Gillman, Meyer Jerison · American Mathematical Monthly May 1961 2,342
2 On Ideal Lattices and Learning with Errors over Rings Vadim Lyubashevsky, Chris Peikert, Oded Regev · Lecture notes in computer science Conference paper 2010 1,835
3 The Zero-Divisor Graph of a Commutative Ring David F. Anderson, Philip S. Livingston · Journal of Algebra Open access Jul 1999 1,350
4 Coloring of commutative rings István Beck · Journal of Algebra Open access Jul 1988 1,234
5 The diamond lemma for ring theory George M. Bergman · Advances in Mathematics Open access Feb 1978 1,174
All 100 most cited papers, with filters and sorting

Where is Rings, Modules, and Algebras research done?

The largest centres of Rings, Modules, and Algebras research in 2022-now 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-now

  1. 1 BaghdadIraq 72 works
  2. 2 TehranIran 55 works
  3. 3 MoscowRussia 49 works
  4. 4 FesMorocco 38 works
  5. 5 BeijingChina 32 works
  6. 6 AligarhIndia 31 works
  7. 7 NanjingChina 28 works
  8. 8 ParisFrance 25 works
  9. 9 KolkataIndia 25 works
  10. 10 IstanbulTürkiye 24 works

Where it is the local speciality

  1. FesMA · 37.6 works36×
  2. AligarhIN · 31.3 works35×
  3. TikritIQ · 21.5 works30×
← 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, Aligarh Muslim University, Cukurova University and Sidi Mohamed Ben Abdellah 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 15.34%fractional works in this field (log) →share of work in the world top 10% →Cukurova UniversityAligarh Muslim Unive…Sidi Mohamed Ben Abd…University of Baghdad
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
1Aligarh Muslim UniversityIndia 68.318.8%42.1×31 +73.7%
2Cukurova UniversityTürkiye 67.732.5%19.1×12 +142.9%
3Sidi Mohamed Ben Abdellah UniversityMorocco 61.58.7%55.6×38 +113.9%
4University of BaghdadIraq 59.58.4%28.1×50 +8.4%
5Lomonosov Moscow State UniversityRussia 59.213.1%9.2×19 +21.0%
6Savitribai Phule Pune UniversityIndia 53.421.3%9.4×10 +59.9%
7Amasya ÜniversitesiTürkiye 52.620.4%52.6×12 +23.4%
8Charles UniversityCzechia 51.519.4%8.8×10 +11.5%
9University of TikritIraq 47.59.2%32.4×22 +53.6%
10University of MonastirTunisia 46.11.6%36.2×14 +74.8%

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 Rings, Modules, and Algebras, country by country

Is Rings, Modules, and Algebras research growing?

Output in 2022-2025 was 13% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Rings, Modules, and Algebras.

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 Rings, Modules, and Algebras as a percentage of every work published that year, 0.012% in 2024.

still counting0.050%0.10%Rings, Modules, and Algebras0.012% in 202519801990200020102020

Fractional works of Rings, Modules, and Algebras 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%Rings, Modules, and Algebras9.8% 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.

Discussion

Ask a question or share a note about Rings, Modules, and Algebras. Posts are plain text and can be reported.