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Everything about Monoid
Algebraic structure with an associative operation and an identity element
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 form a monoid, the identity element being 0. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: MonoidA 5-minute orientation
- Skim a recent paper: On various types of nilpotency of the structure monoid and group of a set-theoretic solution of the Yang–Baxter equationInfluential work since 2022
- Pick up a classic book: Arithmetical Properties of Commutative Rings and MonoidsThe most-reprinted book on the subject
- Read the landmark paper: The dual braid monoidCited 166 times
- Go sideways: SemigroupA closely related topic
- Go sideways: Inverse elementA closely related topic
📖 Definitions
Noun A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.
Adjective Containing only one kind of metrical foot.
🏆 Landmark papers (most cited)
The dual braid monoid
The algebraic Bethe ansatz for rational braid-monoid lattice models
Representations of the rook monoid
Systems of equations over a free monoid and Ehrenfeucht's conjecture
The Monoid of All Injective Order Preserving Partial Transformations on a Finite Chain
The monoid of orientation-preserving mappings on a chain
Complete rewriting systems and homology of monoid algebras
The kernel of monoid morphisms
🆕 Influential since 2022
On various types of nilpotency of the structure monoid and group of a set-theoretic solution of the Yang–Baxter equation
Valuations and the Hopf Monoid of Generalized Permutahedra
The stylic monoid
On the distribution of prime divisors in Krull monoid algebras
A characterization of weakly Krull monoid algebras
📚 Books worth reading
Arithmetical Properties of Commutative Rings and MonoidsScott T. Chapman · 2005
Monoids, acts, and categoriesM Kilʹp, Mati Kilp · 2000
Categories for the working mathematicianSaunders Mac Lane · 1971
Algebraic Monoids, Group Embeddings, and Algebraic CombinatoricsMahir Can, Zhenheng Li · 2014- 📕Free monoids and languagesH. J. Shyr · 1978
Two papersJonathan Leech, J. Leech · 1975- 📕Bimonoids for Hyperplane ArrangementsMarcelo Aguiar, Swapneel Mahajan · 2020
Counter-free automataRobert McNaughton · 1971
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Magma (algebra) In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with…
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