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

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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?

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

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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

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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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### What is known about the algebraic completion of a monoid?

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### Have you ever seen a partial binary operation that is not the morphisms of a semicategory, but it is covered by subsets that are?

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### Extending monoids to a ring

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### Has an “algebraic manifold” been defined before? Are there any non-trivial examples?

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### Has this theorem on cancellative monoid actions been discovered and published?

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### Cancellation property for commutative monoid

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### What is the real name for the initial object in the category of “monoid-valued measures of intervals” on transitive relations?

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### Is every cyclic right action of a cancellative invertible-free monoid on a set isomorphic to the set of shifts of some homography?

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### Is every invertible-free cancellative monoid action represented by “shifting” certain maps?

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### Motivation and reference for Brauer algebras

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### terminology for a kind of two-sided module over a monoid

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### Generalized cancelation properties ensuring a monoid embeds into a group

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### Can every cancellative invertible-free monoid be embedded in a group?

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### Are cofibrations in topological monoids preserved by forming the product with the identity?

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### “Completion property” in $(\beta\omega,+)$

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### Addition and Rudin-Keisler ordering in $\beta \omega$

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### On logarithmic schemes

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### Does every finite poset have a rigid endomorphism?

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### Heuristics for the word problem for monoids

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### Characterizing centralizer of nilpotent self-maps

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### Extending a monoid object in a category

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### Classifying spaces of amalgamated topological monoids

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### On the width of the Catalan monoid and the rank of K-groups of the Furstenberg transformation group

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### Does every set have a rigid self-map?

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