Concepedia

Ideal Theory

Ideal Theory is a branch of abstract algebra that studies ideals—subsets of rings closed under addition and multiplication by ring elements—distinguished by their role in generalizing unique factorization and enabling structural analysis of commutative and noncommutative rings in algebraic number theory and ring theory.

3.8K

Publications

147.4K

Citations

3.4K

Authors

1.3K

Institutions

Publications per year

2017–2026

317

Variants

Theory Of Ideals

Parents

Publications

3.8K

Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra

Choice Reviews Online · 1993 · 2.1K citations

, , +17

The Zero-Divisor Graph of a Commutative Ring

David F. Anderson, Philip S. Livingston · Journal of Algebra · 1999 · 1.3K citations

, , +8

Greobner Bases : an algorithmic method in polynomial ideal theory

Bruno Buchberger · Medical Entomology and Zoology · 1985 · 1.1K citations

, , +11

Ideal vs. Non‐ideal Theory: A Conceptual Map

Laura Valentini · Philosophy Compass · 2012 · 1.1K citations · Full text

, , +9

MULTIPLICATIVE IDEAL THEORY

P. M. Cohn · Bulletin of the London Mathematical Society · 1974 · 1.1K citations

, , +3

1–5 of 3.8K

Authors

3.4K

  1. JH
    Jürgen Herzog

    University of Duisburg-Essen, Germany

    40 publications · 2K citations

    24

    h-index

  2. CH
    Craig Huneke

    Purdue University West Lafayette, United States

    32 publications · 1.5K citations

    22

    h-index

  3. WH
    William Heinzer

    Purdue University West Lafayette, United States

    39 publications · 1.2K citations

    22

    h-index

  4. YB
    Young Bae Jun

    Gyeongsang National University, South Korea

    53 publications · 1.3K citations

    20

    h-index

  5. RG
    Robert Gilmer

    Florida State University, United States

    34 publications · 1.1K citations

    19

    h-index

1–5 of 3.4K

Institutions

1.3K

  1. Purdue University West Lafayette

    West Lafayette, United States

    30 h-index

    98 publications

    3.3K citations

  2. University of Duisburg-Essen

    Essen, Germany

    26 h-index

    61 publications

    2.8K citations

  3. Rutgers, The State University of New Jersey

    New Brunswick, United States

    23 h-index

    48 publications

    2.8K citations

  4. University of Iowa

    Iowa City, United States

    23 h-index

    59 publications

    3.3K citations

  5. Gyeongsang National University

    Jinju-si, South Korea

    21 h-index

    55 publications

    1.7K citations

  6. University of California, Berkeley

    Berkeley, United States

    21 h-index

    45 publications

    2K citations

  7. University of Sheffield

    Sheffield, United Kingdom

    21 h-index

    45 publications

    2.3K citations

  8. University of Michigan

    Ann Arbor, United States

    20 h-index

    40 publications

    2K citations

1–8 of 1.3K

Venues

  1. Journal of Algebra

    270 publications · 12.3K citations

    50

    h-index

  2. Communications in Algebra

    329 publications · 9.8K citations

    47

    h-index

  3. Pacific Journal of Mathematics

    171 publications · 8K citations

    46

    h-index

  4. Transactions of the American Mathematical Society

    TRAN · 192 publications · 8.3K citations

    44

    h-index

  5. Proceedings of the American Mathematical Society

    PROC · 174 publications · 4.6K citations

    36

    h-index

1–5