Most cited papers in Commutative Algebra and Its Applications
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).
Showing 50 of 100 papers. Every paper with more than 242 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Hopf Algebras and Their Actions on Rings Susan Montgomery · Regional conference series in mathematics | 28 Oct 1993 | 2,592 |
| 2 | Computing Persistent Homology Afra Zomorodian, Gunnar Carlsson · Discrete & Computational Geometry | 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 | Apr 1978 | 898 |
| 5 | On the ubiquity of Gorenstein rings Hyman E. Bass · Mathematische Zeitschrift | 1963 | 896 |
| 6 | Gröbner Bases: A Computational Approach to Commutative Algebra Thomas Becker, Volker Weispfenning, Heinz Kredel · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno | 30 Sep 2011 | 766 |
| 7 | Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations Nicolas T. Courtois, A. V. Klimov, Jacques Patarin et al. · Lecture notes in computer science | 2000 | 760 |
| 8 | The Diophantine Equation 8x + py = z2 Qi Lan, Xiaoxue Li · The Scientific World JOURNAL | 2015 | 672 |
| 9 | Rational singularities with applications to algebraic surfaces and unique factorization Joseph D. Lipman · Publications mathématiques de l IHÉS | 7 Jan 1969 | 657 |
| 10 | Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant Edward Bierstone · Inventiones mathematicae | Apr 1997 | 638 |
| 11 | Enumerative tropical algebraic geometry in ℝ² Grigory Mikhalkin · Journal of the American Mathematical Society | 20 Jan 2005 | 621 |
| 12 | Bruno Buchberger’s PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal Bruno Buchberger · Journal of Symbolic Computation | 16 Dec 2005 | 619 |
| 13 | Homotopy properties of the poset of nontrivial p-subgroups of a group Daniel G. Quillen · Advances in Mathematics | May 1978 | 568 |
| 14 | Poly�dres de Newton et nombres de Milnor A. G. Kouchnirenko · Inventiones mathematicae | Feb 1976 | 567 |
| 15 | Intersection theory on algebraic stacks and on their moduli spaces Angelo Vistoli · Inventiones mathematicae | Oct 1989 | 565 |
| 16 | Linear free resolutions and minimal multiplicity David Eisenbud, Shirô Gotô · Journal of Algebra | May 1984 | 518 |
| 17 | Tight closure, invariant theory, and the Briançon-Skoda theorem Melvin Hochster, Craig L. Huneke · Journal of the American Mathematical Society | 1990 | 517 |
| 18 | The number of faces of a simplicial convex polytope Richard P. Stanley · Advances in Mathematics | Mar 1980 | 495 |
| 19 | Completeness Classes in Algebra Leslie Gabriel Valiant · ACM eBooks | 1979 | 489 |
| 20 | The tropical Grassmannian David E Speyer, Bernd Sturmfels · Advances in Geometry | 7 Jul 2004 | 487 |
| 21 | Minimal resolutions of some monomial ideals Shalom Eliahou, Michel A. Kervaire · Journal of Algebra | Feb 1990 | 484 |
| 22 | Families of rationally connected varieties Tom M. Graber, Joe Harris, Jason Starr · Journal of the American Mathematical Society | 29 Jul 2002 | 482 |
| 23 | Preprojective modules over artin algebras Maurice Auslander, Sverre O. Smalø · Journal of Algebra | Sep 1980 | 475 |
| 24 | Generators and relations of abelian semigroups and semigroup rings J�rgen Herzog · manuscripta mathematica | Jun 1970 | 458 |
| 25 | Gröbner bases and primary decomposition of polynomial ideals Patrizia M. Gianni, Barry Trager, Gail Zacharias · Journal of Symbolic Computation | Oct 1988 | 457 |
| 26 | Injective and flat covers, envelopes and resolvents Edgar E. Enochs · Israel Journal of Mathematics | Sep 1981 | 446 |
| 27 | Lectures on matroids W. T. Tutte · Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics | 1965 | 420 |
| 28 | Perpendicular categories with applications to representations and sheaves Werner Geigle, Helmut Lenzing · Journal of Algebra | Dec 1991 | 416 |
| 29 | Some Combinatorial Properties of Schubert Polynomials Sara Billey, William Jockusch, Richard P. Stanley · Journal of Algebraic Combinatorics | Nov 1993 | 403 |
| 30 | ABSOLUTE, RELATIVE, AND TATE COHOMOLOGY OF MODULES OF FINITE GORENSTEIN DIMENSION Luchézar L. Avramov, Alex Martsinkovsky · Proceedings of the London Mathematical Society | 22 Aug 2002 | 395 |
| 31 | Two poset polytopes Richard P. Stanley · Discrete & Computational Geometry | Mar 1986 | 394 |
| 32 | A note on extensions of Baer and P. P. -rings Efraim P. Armendariz · Journal of the Australian Mathematical Society | Dec 1974 | 393 |
| 33 | Homology of Noetherian rings and local rings John Tate · Illinois Journal of Mathematics | Mar 1957 | 392 |
| 34 | On fast multiplication of polynomials over arbitrary algebras David G. Cantor, Erich Kaltofen · Acta Informatica | Jul 1991 | 387 |
| 35 | On graded rings, I Shirô Gotô, Kei-ichi Watanabe · Journal of the Mathematical Society of Japan | Apr 1978 | 387 |
| 36 | Braces, radical rings, and the quantum Yang–Baxter equation Wolfgang Rump · Journal of Algebra | Jun 2006 | 386 |
| 37 | Beck′s Coloring of a Commutative Ring D. D. Anderson, Muhammad Moazzam Naseer · Journal of Algebra | Aug 1993 | 384 |
| 38 | Cohen-Macaulay modules on hypersurface singularities I Horst Kn�rrer · Inventiones mathematicae | Feb 1987 | 372 |
| 39 | ALL MODULES HAVE FLAT COVERS Ladislav Bican, Robert El Bashir, Edgar E. Enochs · Bulletin of the London Mathematical Society | Jul 2001 | 370 |
| 40 | Invariants of finite groups and their applications to combinatorics Richard P. Stanley · Bulletin of the American Mathematical Society | 1979 | 369 |
| 41 | Gromov–Witten theory, Hurwitz theory, and completed cycles Andreĭ Okounkov, Rahul Pandharipande · Annals of Mathematics | Mar 2006 | 366 |
| 42 | P.L. Homeomorphic Manifolds are Equivalent by Elementary 5hellingst Udo Pachner · European Journal of Combinatorics | Mar 1991 | 358 |
| 43 | Idealization of a Module D. D. Anderson, M. Winders · Journal of Commutative Algebra | 15 Dec 2008 | 356 |
| 44 | Multiplication modules Zeinab Abd El-Bast, Patrick P. Smith · Communications in Algebra | 1988 | 355 |
| 45 | Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory Kiumars Kaveh, Askold Georgievich Khovanskii · Annals of Mathematics | 3 Jul 2012 | 353 |
| 46 | Ideals defined by matrices and a certain complex associated with them J. A. Eagon, Douglas Geoffrey Northcott · Proceedings of the Royal Society of London A Mathematical and Physical Sciences | 11 Sep 1962 | 346 |
| 47 | On the Ideal Theory of Graphs Aron Simis, W.V Vasconcelos, Rafael H. Villarreal · Journal of Algebra | Jul 1994 | 341 |
| 48 | Finiteness properties of local cohomology modules (an application ofD-modules to commutative algebra) Gennady Lyubeznik · Inventiones mathematicae | Dec 1993 | 340 |
| 49 | On the derived categories of coherent sheaves on some homogeneous spaces Mikhail M. Kapranov · Inventiones mathematicae | Oct 1988 | 340 |
| 50 | Some Algebras Associated to Automorphisms of Elliptic Curves Michael Artin, John Tate, Michel Van den Bergh · Modern Birkhäuser classics | 2007 | 339 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.