Tagged Questions

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.

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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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Maximal group image!

How does one prove: if $S$ is a finitely generated Clifford semigroup its maximal group image is actually $S_{e_{n}}$?
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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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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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Sets of natural numbers such that sums of a bounded number of its elements form a semigroup

This is a naive question and I'm afraid it might be better placed on math.se. I would like to leave it to your judgement. I would like to know what is known about sets $A$ of natural numbers such ...
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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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What is the combinatorial data classifying non-normal affine toric varieties?

Recall that a toric variety is a variety $V$ containing an open dense algebraic torus. Here an algebraic torus means a finite product of copies of the multiplicative group of the ground field (which I ...
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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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Is every $n$-ary semigroup a subalgebra of an algebra derived from a binary semigroup?

Let $(A,f)$ be an $n$-ary semigroup ($n \ge 2$). Then there exists a ($2$-ary) semigroup $(\overline A,*)$ with an inclusion homomorphism $A \hookrightarrow \overline A$ such that that the restriction ...
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Can a semigroup be defined on a Banach algebra? [closed]

I simply need to know that how a semigroup of operators (say $\{T(t)\}_{t\geq 0}$) is defined on any Banach algebra (say $X$)? For $(f,g\in X)$ now the so called product is also there i.e. $f.g\in X$. ...
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Airy's equation on $\mathbb R_-$

I am interested in Airy's equation $$\frac{\partial u}{\partial t}(t,x)=-\frac{\partial^3 u}{\partial x^3}(t,x)$$ on a bounded or semi-bounded domain, e.g. on $(-\infty,0)$. In order to obtain a group ...
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Projective limit construction of a semigroup

Let $\tilde{\mathbb N}$ be the Abelian semigroup (under addition) given by $\mathbb N\cup\{0,\infty\}$, and let $S_n$ be the Abelian monoid $\tilde{\mathbb N}^{2^n}$ under point-wise addition. ...
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Heat semigroup ultracontractive?

Let $g(x,t)= \frac{1}{(4 \pi t)^{\frac{n}{2}}}e^{\frac{-|x|^2}{4t}}$ be the heat kernel on $\mathbb{R}^{n}.$ Is the standard definition now to say that this heat-semigroup $T(t)(f):=g *f(.,t)$ is ...
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Restriction of a semigroup to a form domain

Say, we have a Hilbert space $H$ with a semibounded self-adjoint operator $A:D(A)\to H$ generating a strongly continuous semigroup $T(t):H\to H$. Is it possible to restrict $T(t)$ to a form domain of ...
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Why semigroups could be important?

There is known a lot about the use of groups -- they just really appear a lot, and appear naturally. Is there any known nice use of semigroups in Maths to sort of prove they are indeed important in ...
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A generalisation of $C_0$-semigroups

A $C_0$-semigroup is a strongly continuous family $\{T(t)\}$ of bounded linear operators on a normed space $X$, indexed in $\mathbb R_+$ and with two additional properties that make it look like an ...
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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 $\ell(R/\... 2answers 286 views Proving that a semigroup is regular In a number of diverse situations of interest to me (mostly associated with something called the abelian sandpile model), one can define a nonabelian semigroup generated by commuting elements$a_1,\...
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 ...