Questions tagged [semigroups]

Question 1

This old question asks for an example of a semigroup $(G, \ast)$ for which (a) $G$ has a left identity, i.e., an element $e \in G$ such that $e \ast g = g$ for all $g$, and (b) every element of $G$ ...

Question 2

According to a German textbook there are many semigroups $(G,\odot)$ with the following properties: (1) $|G|>2$. (2) There is a left identity element $e\in G$, that is $e\odot g=g$ for all $g\in G$....

Question 3

I have been looking into undecidable groups, and was shown this presentation: {\begin{array}{lllll}\langle &a,b,c,d,e,p,q,r,t,k&|&&\\&p^{10}a=ap,&pacqr=rpcaq,&ra=ar,&\\&...

Question 4

I am working with parametrized polynomial plane curves and I have several related questions about Milnor numbers and singularities. I would be grateful for references, precise statements (theorem ...

Question 5

I have already solved this problem: Suppose that a minimal left ideal $L$ of a semigroup is commutative. Prove that $L$ is a group. My question is how to solve this harder problem: Let $S$ be a ...

Question 6

I'm trying to understand the proof that idempotent elements commute in an inverse semigroup, but first I need to understand this lemma about the inverse of a product, which is apparently the same as ...

Question 7

Recently, I've been studying non-autonomous parabolic problems and, as a consquence, the non-autonomous version of semigroups, evolution operators, has appeared. I'm very interested in how resolvent ...

Question 8

Suppose $f$ and $g$ are operators. If for all $x$, we have $f(g(x))=f(x)$ and $g(f(x))=g(x)$ (an example: $f$ is relative interior, $g$ is closure, and $x$ is convex set), then is there a term to ...

Question 9

Given a family of Markov processes $ \{ ( X_{ t} ^{ x})_{ t \geqslant 0}\colon x \in E \}$, where $ X_{ t} ^{ x}$ denotes a time-homogeneous Markov process starting at $ x \in E$, I'm trying to show ...

Question 10

Are there examples of commutative and associative binary operations over $\mathbb R$ that cannot be expressed as $x \oplus y = f^{-1}(f(x)+f(y))$ where $f$ is an invertible function $f:\mathbb R\...

Question 11

I am exploring the following question: Does there exist an associative binary operation (i.e., a semigroup) on a set ( G ) that has at least a right identity and such that every element has at least ...

Question 12

Let $X$ be an infinite abelian semigroup and fix a finite subset $S\subseteq X$. Question. Is it true that there exist $x,y \in X$ such that $\{x,x+y,x+2y\}\cap S=\emptyset$? Ps. It would be enough ...

Question 13

I’m reading nonlinear evolution equations by Song-Mu Zheng and I have some questions regarding the following statement THEOREM 2.4.1 ; COROLLARY 2.4.1 ; COROLLARY 2.4.2 ; COROLLARY 2.4.3 All are ...

Question 14

Let $G$ be a finitely-generated subgroup of $\mathbb{Z}^n$ and $A$ a finitely-generated sub-semigroup of $\mathbb{N}^n$ (which contains $(0,\ldots,0)$). Say I have fixed generating sets $g_1,\ldots,...

Question 15

I am looking at the textbook by Bakry, Gentil, and Ledoux "Analysis and Geometry of Markov Diffusion Operators". This discussion is from section 3.1.6 which does not show computations and I ...

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Questions tagged [semigroups]

What is an example of a finite, indecomposable semigroup with left identity and right inverses other than the basic example $g \ast h := h$?

Semigroup that is not a group [duplicate]

Does anyone know how the finitely presented undecidable group (shown in Collins, Donald J. (1986)) works?

Milnor number parity and singularities of parametrized plane curves

Semigroups help on commutative groups

Proof that $(ab)^{-1} = b^{-1}a^{-1}$ in an inverse semigroup $S$.

Evolution operators reference request

What is the term to describe this relationship?

Semi-group property for homogeneous Markov processes

Commutative and associative binary operations over $\mathbb R$

Is it possible to have a semigroup with a right identity where left inverses are not unique?

$x,x+y,x+2y$ in a cofinite subset of an abelian semigroup

nonlinear evolution equations by Song-Mu Zheng Uniqueness of inhomogeneous PDE semigroup theory

Semigroup generating sets for a group intersected with a semigroup

Derivative of Semigroup

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