Key papers in Algebra and Number Theory
Pofolia’s corpus holds 68 papers from the Algebra and Number Theory subfield (2012–2022). The list below starts with the most cited.
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”.
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.
Foundations of Module and Ring Theory
2018 · 1,082 citations
This volume offers a comprehensive introduction to module and ring theory, presenting original and recent results with complete proofs.
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.
Modular Lie Algebras and their Representations
2020 · 464 citations
This book offers an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Recently added
Model Theoretic Algebra with particular emphasis on Fields, Rings, Modules
2022 · FWCI 4.57 · 162 citations
This volume bridges model theory and algebra, offering a definitive account of algebraically compact modules, crucial for both fields.
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.
Renormalising SPDEs in regularity structures
Journal of the European Mathematical Society · 2020 · Q1 · SJR 3.00 · FWCI 29.46 · 130 citations
A new formalism constructs a renormalization group action on singular stochastic PDEs, showing BPHZ-lifted solutions match modified classical PDE solutions.
Linear Algebra over Commutative Rings
2020 · 168 citations
This monograph introduces matrix theory over commutative rings and discusses the structure theory of projective modules.
Modular Lie Algebras and their Representations
2020 · 464 citations
This book offers an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic.
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