# Questions tagged [semigroups]

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). Of course, any monoid or group is also a semigroup.

281 questions
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### Compactness of semigroups, boundary conditions

I have a question about compactness of semigroups and boundary conditions. Let $\Omega$ be an unbounded domain of $\mathbb{R}^d$ with smooth boundary and $m(\Omega)=\infty$. Then we can define two ...
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### Short time $L^1$ bounds for semigroups obtained from elliptic operators

Let $\Omega$ be a domain in $\mathbb{R}^n$ with smooth boundary, and let $L$ be a negative definite second order elliptic differential operator defined with $\mathcal{D}(L) \subset H^2(\Omega)$, given ...
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### Have semigroups with actions on themselves that have a dual to the compatibility axiom ever been studied?

For a semigroup $G$ with a left action on itself, the axiom for compatibility becomes: $$\forall f,g,h\in G:hg(f)=h(g(f))$$ Now suppose there is additional axiom, or constraint if you prefer, ...
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### Can a semigroup with zero be globally isomorphic to a semigroup without zero?

This is not a great question for sure and it may even be trivial for all I know, but a couple of years ago, when I still thought I'd be a mathematician, I spent quite a lot of time thinking about it ...
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### What is known about semigroups that are generated by (cyclic) subgroups?

A semigroup $(A,\cdot)$ that is idempotent (i.e. $a^2=a$ for every element $a\in A$) is naturally generated by its subgroups (every element on itself constitutes a trivial group). I would like to know ...
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### On extending a semigroup property

Let $T(t)$ be a $C_0-$semigroup on a Hilbert space $H$ with a generator $A$. It is well known that for all $x\in H,$ we have: $\int_0^t T(s)x ds \in D(A)$ and $A\int_0^t T(s)x ds = T(t)x-x$. How ...
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### Embedding a cancellative monoid into another in such a way that $|X-x|=|X|$, where $X$ is a fixed finite set and $x\in X$

Preliminaries. Let $\mathbb A = (A, +)$ be a possibly non-commutative semigroup. For $X, Y \subseteq A$ we set $$X - Y := \{a \in A: a + y \in X\text{ for some }y \in Y\},$$ which is just the usual ...
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### Embedding a cancellative monoid into another in such a way that a prescribed element becomes left-invertible

Let $\mathbb A = (A, +_A)$ be a cancellative, but possibly non-commutative, monoid with identity $0$, and fix an element $x \in A$. Does there always exist a cancellative monoid $\mathbb B = (B, +)$ ...
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### Embedding abelian cancellative Hausdorff topological semigroups into abelian Hausdorff topological groups

An abelian cancellative semigroup embeds (via a semigroup monomorphism) into an abelian group. What about an abelian cancellative Hausdorff topological semigroup that does not embed (via a ...
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### Factorization of the Fokker-Planck semigroup

I have posted this question on stackexchange over four month ago, but didn't get an answer: "In the classical theory of Markov processes, the Fokker-Planck semigroup $\{T_t:t\ge 0\}$ can be factored ...
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Let $f(z,a)$ be an analytic function on $C^+=\{\Re z>0\}$ for each fixed $a>0$, and we have the following (weaker) estimates $$|f(re^{i\theta},a)|\leq C (r\cos\theta)^{-n}, ~~~r>0,-\frac{\pi}... 1answer 308 views ### Cancellable elements of a power semigroup For a semigroup S, its power semigroup P(S) is the semigroup of all non-empty subsets of S with the operation given by AB=\{ab\,|\,a\in A,b\in B\}. I would like to know about the cancellable ... 0answers 126 views ### On the computational complexity of the Hilbert polynomial of numerical semigroup rings Let (R, \mathfrak{m}) = k[[X^a, X^b, X^c]], a<b<c, gcd(a, b, c) = 1, be a semigroup ring. We have R is a Cohen-Macaulay local ring of dimension one. It is well known that \ell(R/\... 1answer 130 views ### Non-idempotent ultrafilters in the Stone-Cech compactification Supposing that \Gamma is an infinite, discrete group and that \beta\Gamma is the Stone-Cech compactification of \Gamma, the group structure of \Gamma can be extended to a semigroup structure ... 0answers 108 views ### dual composition of binary relations I'm not sure if this is of any interest at all, but I spent some time looking at it a couple of years ago so I'd like to ask for input on this. Given two binary relations \rho,\,\sigma on a set X,... 0answers 78 views ### Lower periodic subsets of groups and semigroups Suppose that A and B are subsets of a group or semigroup. We call A left upper [resp. lower] B-periodic if BA\subseteq A [resp. A\subseteq BA]. If A is both left upper and lower B-... 1answer 71 views ### Cosets of the fixer of an action of a monoid on a finite set Let M be a monoid that acts transitively from the right on a finite set X. Assume furthermore that the action of M on X induces for every m \in M a bijection on X \to X, x \mapsto x.m. Let ... 0answers 113 views ### Pseudovarieties of monoids All (pseudo)varieties considered here are (pseudo)varieties of monoids. It is known that any (finite or infinite) monoid that satisfies the identities xhxyty = xhyxty, \quad xhytxy=... 1answer 108 views ### C_0 semigroups on parameterized Banach spaces or moving domains Is there any literature corresponding to one or two-parameter semigroups such that eg. T(t) \in \mathcal{L}(X(t)) or T(s,t) \in \mathcal{L}(X(t),X(s)) for parameterized Banach spaces X(t)??? I ... 0answers 93 views ### Semigroups on Banach Lattice Let \{Z(t)\}_{t\geq 0} be a semigroup of positive operators on a Banach lattice X. I want to show that$$\int_0^1[Z(1-s)+Z(1+s)]fds-f\in X_+,\quad f\in X_+ Where $X_+$ denotes the positive ...
Let $(S,\le)$ be a distributive lattice. Is there a semigroup structure on $S$ such that $S$ is cancellative and always $(x\wedge y)(x\vee y)=xy$?