# Questions tagged [semigroups-and-monoids]

A semigroup is a set $S$ together with a binary operation that is associative. Examples of semigroups are the set of finite strings over a fixed alphabet (under concatenation) and the positive integers (under addition, maximum, or minimum). A monoid is a semigroup with a neutral element. Of course, any group is also a monoid/semigroup.

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### What is the correct name for a “product function” on a monoid?

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### Maximal number of commuting functions of a finite set

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### The rank of a semigroup

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### Combinatorial proof of invertibility of a symmetric matrix associated to the ring of matrices over a finite field

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### Centralizer of a single element in the monoid of self-maps of a set

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### For what sets $X$ do there exist a pair of functions from $X$ to $X$ with the identity being the only function that commutes with both?

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### A semifield of characteristic zero may have a finite number of elements

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### Are most semigroups nilpotent of degree 3?

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### Question on monoid algebras

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### Bijection between monoid of nilpotent decreasing self-maps and local subsemigroup

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### What spaces $X$ do have $\text{End}(X) \cong \text{End}(\mathbb{R})$?

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### Spaces with unique endomorphism monoids

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### Quasi-isometries and E-unitary inverse semigroups

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### Ascending sequences of idempotents in inverse semigroups

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### On the number of connected functional digraphs recoverable from the preimage set size structure

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### Additivity of the upper Banach density

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### What is a “cusp” (“кусок”) in relation to Guba's embedding theorem?

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### Is the natural action of the monoid of endomorphisms is a complete invariant for group?

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### Classification of associative polynomial functions

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### Associativity may fail by little?

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### Closed submonoid of $(\mathbb{C}^*)^n$

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### Closed cobounded additive submonoid of $\mathbb{R}^n$

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### What is the minimal possible size of a subset of this semigroup satisfying the following conditions?

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### Counting nilpotent self-maps of $\{1,\dots,n\}$ with image of a given cardinal

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### Comonoids in the category of monoids

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### Compute irreducibles of monoid

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### Continuous semigroup homomorphism of composition to additive structure

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### Monoids of endomorphisms of nonisomorphic groups

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### Internal commutative monoid gives commutative monad

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### Joint spectral radius of $\{M,M^T\}$

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### Cancellativity of a particular $2$-generated monoid presented by an infinite number of relations

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### Are there finitely-presented astral monoids?

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### $m$-potent elements in $N(C_n)$

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### Generating the monoid of injective endomorphisms of the free group

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### Define a homomorphism of a set of graphs to its power set

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### Multiplicative monoid of ring modulo units

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### Generalization of pseudogroups

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### Is the equational theory of groups axiomatized by the associative law?

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### A characterisation of faces of rational polyhedral cones

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### Which homotopy types can be realized as the classifying space of a right-cancellative discrete monoid?

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### Who invented Monoid?

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### Topological category of topological monoids / operads

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### Characterization of Archimedean linearly ordered monoids

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### Special monomorphism to encode the inclusion of topological submonoids

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### How exactly to adapt Brown's collapse from monoids to algebras?

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### Primage structures: induced domain partitioning by itterated inverse (reference request)

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### A question about semigroup union

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### What is the normalized complex of a simplicial set with a monoid action?

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### Category of continuous self maps

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