# 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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### Nonzero idempotents in compact semitopological semigroups with zero

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### Matrix decompositions as monoid isomorphisms. Ever considered before?

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### Semigroup ideals of a ring or an algebra

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### The "matrix direct sum" monoid modulo unitary equivalence

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### Factoring a function from a finite set to itself

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### Can you cancel powers in equalities of powers of big enough elements in a commutative finitely presented monoid?

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### Is a solvable group satisfying a semigroup law?

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### Isomorphic morphisms. A 27-morphism category

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### Computationally intractable orbit of a monoid action on a finite set

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### Can the relation between count of commuting pairs and conjugacy classes for finite groups be generalized to semigroups?

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### Submonoid of free monoid with certain properties

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### What is the precise connection between logarithmic algebraic geometry and the field with one element?

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### Are there any interesting noncommutative monoid bihomomorphisms?

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### Partitions of a union of complete graphs into independent sets

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### Effect on finite transformation semigroup under a particular modification of the generators

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### More vocabulary for periodic elements in monoids

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### Functions over monoids which factor in two different ways

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### First isomorphism theorem for inverse semigroups together with v-prehomomorphisms?

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### What is this algebraic object (special case of a semigroup)?

**3**

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### Functors that preserve monoids

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### Terminology for a ring where every right cancellable element is cancellable

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### Terminology for an kind-of principal fibration

**3**

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### An integral transform and the Stone-Weierstrass theorem

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### Partial orders on $\mathbb{N}^m$ compatible with addition

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### Why $\beta S$ is not a semigroup when $S$ is a (directed) partial semigroup?

**3**

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### Cohomology of commutative monoid acting on module

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### Are there overwhelmingly more finite monoids than finite spaces? [closed]

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### Terminology and notation for generated subgroups

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### Free monoids on posets

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### When is the submonoid preserving a subspace finitely generated?

**12**

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### Is the Petersen graph a "Cayley graph" of some more general group-like structure?

**3**

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### Lax monoidal functor

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### Are there any "simple" monoids with intermediate growth?

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### Size of the kernel (minimal ideal) of a finite semigroup

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### The forgetful functor from Groups to Semigroups

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### Is the group ring of an amenable group, viewed as multiplicative monoid, amenable?

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### Derivable relations in a monoid

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### Quotient of monoids and monoid algebras

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### Cuntz semigroups of basic C*-algebras

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### Do you know rings without involutions, auto-anti-isomorphics? In that case, what is the minimal example?

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### Monoids with three or more "natural" partial orders

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### Well-foundedness of divisibility vs well-foundedness of right- and left-divisibility

**3**

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### Is it true that the structure of a commutative ordered semiring is unique on a commutative ordered monoid?

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### Computations of divisor class monoids

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### Reference request: a cousin to the log semiring

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### Is each squared finite group trivial?

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### Flag variety as monoid and Schubert calculus

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### Cayley's theorem for regular semigroups

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### Conjugacy classes of monoids II: Abelianising a monoid, wrongly

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