Everything about Semigroup

🧭 Start here: a 6-step reading path

1. Read the overview: SemigroupA 5-minute orientation
2. Skim a recent paper: Semigroup-based theoretical prospects on optimal control of stochastic second-order Gurtin–Pipkin integro-differential equationsInfluential work since 2022
3. Pick up a classic book: Functional analysis and semi-groupsThe most-reprinted book on the subject
4. Read the landmark paper: Generators and relations of abelian semigroups and semigroup ringsCited 323 times
5. Go sideways: MonoidA closely related topic
6. Go sideways: Semigroup with involutionA closely related topic

🏆 Landmark papers (most cited)

• Generators and relations of abelian semigroups and semigroup rings

  J�rgen Herzog · 1970 · Manuscripta Mathematica · 323 citations

• Analyticity of the semigroup generated by the Stokes operator inL r spaces

  Yoshikazu Giga · 1981 · Mathematische Zeitschrift · 296 citations

• Graph and semigroup homomorphisms on networks of relations

  Douglas R. White, Karl P. Reitz · 1983 · Social Networks · 278 citations

• The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction–diffusion equations

  Cheng-Kui Zhong, Mei-Hua Yang, Chun-You Sun · 2006 · Journal of Differential Equations · 233 citations

• THE PROBLEM OF SOLVABILITY OF EQUATIONS IN A FREE SEMIGROUP

  G S Makanin · 1977 · Mathematics of the USSR-Sbornik · 218 citations

• Pointwise semigroup methods and stability of viscous shock waves

  Kevin Zumbrun, Peter Howard · 1998 · Indiana University Mathematics Journal · 214 citations

• The natural partial order on a regular semigroup

  K. S. Subramonian Nambooripad · 1980 · Proceedings of the Edinburgh Mathematical Society · 189 citations

• The Subsemigroup Generated By the Idempotents of a Full Transformation Semigroup

  J. M. Howie · 1966 · Journal of the London Mathematical Society · 177 citations

🆕 Influential since 2022

• Semigroup-based theoretical prospects on optimal control of stochastic second-order Gurtin–Pipkin integro-differential equations

  K. Anukiruthika, P. Muthukumar, Pratibhamoy Das · 2025 · Optimization · 28 citations

• Nonfinitely based ai-semirings with finitely based semigroup reducts

  Marcel Jackson, Miaomiao Ren, Xianzhong Zhao · 2022 · Journal of Algebra · 22 citations

• Dynamical generalizations of the prime number theorem and disjointness of additive and multiplicative semigroup actions

  Vitaly Bergelson, Florian K. Richter · 2022 · Duke Mathematical Journal · 18 citations

• Sombor Index over the Tensor and Cartesian Products of Monogenic Semigroup Graphs

  Seda Oğuz Ünal · 2022 · Symmetry · 15 citations

• A semigroup method for high dimensional elliptic PDEs and eigenvalue problems based on neural networks

  Haoya Li, Lexing Ying · 2022 · Journal of Computational Physics · 14 citations

📚 Books worth reading

• Functional analysis and semi-groupsEinar Hille · 1948
• 📕Monoidal TopologyDirk Hofmann, Gavin J. Seal · 2014
• Semigroup theory and its applicationsA. H. Clifford, Karl Heinrich Hofmann · 1996
• PolugruppyE. S. Li͡apin · 1960
• Continuous semigroups in Banach algebrasAllan M. Sinclair · 1982
• 📕Analytic Methods for Coagulation-Fragmentation Models, Volume IJacek Banasiak, Wilson Lamb · 2019
• Completely regular semigroupsMario Petrich · 1999
• 📕Convergence of One-Parameter Operator SemigroupsAdam Bobrowski · 2016

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

• Monoid In abstract algebra, a monoid is a set equipped with an associative binary operation and an identity element. For example, the natural numbers with addition…
• Semigroup with involution In mathematics, particularly in abstract algebra, a semigroup with involution, or a *-semigroup, is a semigroup equipped with an involutive anti-automorphism…
• Semilattice In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset…
• Inverse semigroup In semigroup theory, an inverse semigroup (occasionally called an inversion semigroup) S is a semigroup in which every element x in S has a unique inverse…
• Inverse element In mathematics, the concept of an inverse element generalises the concepts of opposite (−x) and reciprocal (1/x) of numbers. Given an operation denoted…
• Free monoid In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that…
• Homomorphism In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector…
• Semigroup with three elements In abstract algebra, a semigroup with three elements is an object consisting of three elements and an associative operation defined on them. The basic…