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Algebra and Number Theory papers

Pofolia’s corpus holds 67 papers from Algebra and Number Theory (2012–2026), each with a short summary. Below, the 20 most-cited, then the most recently added.

At a glance

  • Most cited: Introduction To Commutative Algebra (2018, 3,041 citations).
  • The 20 papers listed have 8,705 citations between them.
  • 4 of the 6 with a known journal quartile appeared in a Q1 journal.
  • 8 have a free full text (open access).
  • Most frequent journals: Annals of Mathematics, Cambridge University Press eBooks, Advanced studies in pure mathematics.
  • Published between 2012 and 2021.

Most cited

Ranked by citation count. Because citations accumulate over time, this list naturally leans towards work published a few years ago; for where the field is now, see “recently added”. How to read the signals

  • Introduction To Commutative Algebra

    2018 · FWCI 25.88 · 3,041 citations

    This abstract outlines the foundational topics covered in an introductory text on commutative algebra, detailing key areas such as rings, ideals, modules, and dimension theory.

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  • Bounded gaps between primes

    Annals of Mathematics · 2014 · Q1 · SJR 9.00 · FWCI 88.03 · 464 citations · Open access

    Mathematicians have proven that the gap between consecutive prime numbers is bounded, specifically showing that there exists a prime pair with a difference less than 71 million.

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  • Semisimple Subalgebras of Semisimple Lie Algebras

    Digital Commons - USU (Utah State University) · 2020 · FWCI 12.04 · 463 citations · Open access

    This thesis introduces a software toolkit for classifying subalgebras of Lie algebras, specifically focusing on those isomorphic to sl(2) and regular subalgebras.

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  • Nilpotent Orbits in Semisimple Lie Algebras

    2017 · FWCI 11.04 · 401 citations

    This book synthesizes key results on classifying and understanding nilpotent orbits in complex semisimple Lie algebras, connecting them to Weyl group representations and primitive ideals.

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  • Identical Relations in Lie Algebras

    2021 · FWCI 3.58 · 368 citations

    This work delves into the fundamental theory of Lie algebras, focusing on concepts like free Lie algebras, homogeneous structures, and varieties of Lie algebras.

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  • Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory

    Annals of Mathematics · 2012 · Q1 · SJR 9.00 · FWCI 35.03 · 350 citations · Open access

    This paper introduces Newton-Okounkov bodies, generalizing Newton polytopes, for integral point semigroups, graded algebras, and linear series on varieties.

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  • Small gaps between primes

    Annals of Mathematics · 2014 · Q1 · SJR 9.00 · FWCI 61.07 · 309 citations · Open access

    A refined sieve method demonstrates that the prime k-tuples conjecture holds for a positive proportion of admissible k-tuples, proving that the infimum of gaps between consecutive primes is bounded.

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  • On the generalized Apostol-type Frobenius-Euler polynomials

    Advances in Difference Equations · 2013 · FWCI 52.89 · 309 citations · Open access

    New identities for generalized Frobenius-Euler polynomials are derived, establishing a connection between these polynomials and the generalized Hurwitz-Lerch zeta function at negative integers.

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  • Lie Superalgebras and Enveloping Algebras

    Graduate studies in mathematics · 2012 · FWCI 4.23 · 291 citations

    This book develops the theory of Lie superalgebras and their enveloping algebras, extending classical Lie algebra concepts to a broader mathematical framework with applications in various fields.

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  • Regularized SCAN functional

    The Journal of Chemical Physics · 2019 · Q1 · FWCI 40.81 · 285 citations · Open access

    A modified version of the SCAN density functional has been developed to eliminate numerical instabilities, enabling reliable pseudopotential generation.

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  • Catalan Numbers

    Cambridge University Press eBooks · 2015 · FWCI 0.86 · 277 citations

    This book offers the first comprehensive collection of Catalan numbers, detailing their properties and applications across diverse mathematical fields like combinatorics, algebra, and probability.

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  • A Course in Model Theory

    Cambridge University Press eBooks · 2012 · FWCI 4.43 · 269 citations

    This book offers a concise introduction to model theory, progressing from fundamental concepts to advanced topics like stability and Hrushovski constructions.

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  • Nonlinear poisson brackets: geometry and quantization

    2012 · FWCI 12.88 · 265 citations

    This book introduces new mathematical objects to construct Lie group analogs for nonlinear Poisson brackets and address quantization problems in semiclassical approximations.

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  • PolyLogTools — polylogs for the masses

    Journal of High Energy Physics · 2019 · Q2 · FWCI 44.03 · 262 citations · Open access

    A new Mathematica package, PolyLogTools, is introduced to implement algorithms for computing and analyzing multiple polylogarithms, essential for Feynman integral calculations.

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  • Gradings on Simple Lie Algebras

    Mathematical surveys and monographs · 2013 · FWCI 9.12 · 246 citations

    This monograph provides a self-contained exposition and classification of gradings by arbitrary groups on classical simple Lie algebras, particularly in characteristics other than 2.

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  • Frames and Locales: Topology without points

    2012 · 228 citations

    This work introduces and explores the mathematical framework of frames and locales, a point-free approach to topology that redefines spatial concepts without relying on individual points.

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  • Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms

    2013 · FWCI 44.19 · 225 citations

    This paper systematically explores the algorithmic and analytic properties of generalized harmonic sums (S-sums), which appear in high-energy physics calculations and combinatorial problems. It establishes a connection between S-sums and generalized harmonic polylogarithms via Mellin transforms.

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  • Algebraic Spaces and Stacks

    Colloquium Publications - American Mathematical Society/Colloquium Publications · 2016 · FWCI 9.47 · 222 citations

    This book introduces graduate students and researchers to the theory of algebraic spaces and stacks, building upon foundational concepts in algebraic geometry.

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  • Uniform bounds and symbolic powers on smooth varieties

    2012 · 219 citations

    Multiplier ideals establish effective uniform bounds on the multiplicative behavior of ideal sheaves on smooth algebraic varieties, leading to a surprising result on symbolic powers of radical ideals.

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  • Differential Systems Associated with Simple Graded Lie Algebras

    Advanced studies in pure mathematics · 2018 · Q3 · 211 citations · Open access

    This survey paper introduces the Lie algebra of infinitesimal automorphisms of differential systems (M, D), where D is a subbundle of the tangent bundle T(M).

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Recently added

Journals in this field

The journals that publish most of this field’s papers. Quartile (Q1–Q4), SJR and h-index are from SCImago Journal Rank; “in this field” is how many of the journal’s pooled papers belong here. What is a Q1 journal? · What is the h-index?

JournalQuartileSJRh-indexIn this fieldSummaries
Annals of MathematicsQ19.00153525
Proceedings of the London Mathematical SocietyQ12.006934
AsterisqueQ2—5534
Advanced Studies in Pure MathematicsQ3—738
Journal of High Energy PhysicsQ2—279219
Duke Mathematical JournalQ14.0010515
Journal of the European Mathematical SocietyQ13.007314
Physical Review LettersQ12.00750145

Every journal in Algebra and Number Theory (Q1–Q4) →

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