# Tagged Questions

A semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup with an identity element is called monoid. This tag is most frequently used for questions related to the concept of semigroups in the context of abstract algebra. Please use the more ...

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### Are there any resources on this notion of a “directed” semigroup?

Given two additive semigroups $G$ and $H$, and a semigroup action $\& : G \times H \to G$, then intuitively $H$ can be thought of as a set of "directions" in which we can move in the space $G$. ...
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### Free idempotent semigroup with 3 generators

On Finite free objects I asked examples of finite free objects. I got answer "The free idempotent semigroup satisfies $x^2=x$ for each element $x$. And I confirm it is finite if it is finitely ...
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### Computing the shortest encoding for a transformation

Here goes... Let $n = 2^p$ for some $p \in \mathbb{N}$. Let $\mathcal{T}_n$ denote the set of all transformations on $\mathbb{Z}_n$ (viz. the transformation monoid). Pick $C$ to be an order ...
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### Are there any other useful semigroups aside from $e^{At}$

$e^{At}$ trivially satisfies both properties of semigroup namely $T(t+s) = T(t)T(s)$ $T(0) = I$ Does there exist any other commonly used operators aside from $e^{At}$ that is a semigroup? ...
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### Build a Markov process from a transition semigroup

Suppose that we have a Markov process $X$ with time-homogeneus transition probability function given by $p(t,x,A)$, with $t>0, x\in E, A \in \mathcal E$, where $(E,\mathcal E)$ is the state space. ...
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### Order of calculation in a Semigroup.

If $(A,\cdot)$ is a semigroup, i.e. if we have: $\forall (x,y,z)\in A^{3}, (x\cdot y)\cdot z=x\cdot(y\cdot z)$, then the order of calculations doesn't matter no matter the number of factors and we can ...
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### Is there a name for this property?

Is there a general name for the following properties, (similar to the properties of existence of an additive identity, existence of multiplicative identity etc): For any given set, the intersection ...
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### Infinitesimal Generator of Ito Diffusion Process

Suppose one has the an Ito process of the form: $$dX_t = b(X_t)dt + \sigma(X_t)dW_t$$ The following is an excerpt from wikipedia My question is on how to derive this operator? It looks very ...
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### Calculating the generator of a weighted transition function

Let $(P_t)_t$ be the transition function of a Feller-Dynkin process $X$. The usual Banach space of functions that the semigroup $(P_t)_t$ is working on is $C_0(E)$, i.e. continuous functions that ...
### Let $G$ be a semigroup. If for any $a,b\in G$, the equations $ax=b$ and $ya=b$ are solvable, then $G$ is a group.
I at a loss here. Showing that $G$ has an identity is the difficult part here. Obviously for each $a\in G$ there are $b,c\in G$ such that $ab=a$ and $ca=a$, but I need a hint as to how to prove these ...