Question

Why do $ \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}$ and $ \begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix}$ generate a free semigroup?

score 100 · Answer 1 · 2021-06-20 11:53:56

100

Views

Why do $ \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}$ and $ \begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix}$ generate a free semigroup?

Published on 20 Jun 2021 - 11:53

score 42 · Answer 2 · 2026-02-24 05:12:03

42

Views

Is there a compact set $S$ in topological semigroup $T$ with $t^{-1}K\subseteq S$, where $K$ is compact set in $T$?

Published on 24 Feb 2026 - 5:12

score 120 · Answer 3 · 2026-03-29 07:31:26

120

Views

What type of property for subsemigroups or submonoids is this?

Published on 29 Mar 2026 - 7:31

score 74 · Answer 4 · 2026-03-29 05:49:42

74

Views

Cartesian product of finitely generated integral monoids

Published on 29 Mar 2026 - 5:49

score 32 · Answer 5 · 2026-02-24 05:12:30

32

Views

$|F\cap K^{-1}A|\leq \sum_{k\in K}|F\cap k^{-1}A|$?, where $K$ is compact set, $F$ is finite set in topological semigroup $T$

Published on 24 Feb 2026 - 5:12

score 95 · Answer 6 · 2021-07-06 09:21:12

95

Views

Markov chain semigroup: action on densities

Published on 06 Jul 2021 - 9:21

score 95 · Answer 7 · 2021-07-11 13:12:08

95

Views

Second isomorphism theorem for semigroups

Published on 11 Jul 2021 - 13:12

score 62 · Answer 8 · 2026-03-25 08:12:59

62

Views

First isomorphism theorem for inverse semigroups together with v-prehomomorphisms?

Published on 25 Mar 2026 - 8:12

score 85 · Answer 9 · 2026-03-29 05:44:10

85

Views

Is there a standard notation for the collection $\{R\cap S:R\in\pi,S\in\sigma\}$ where $\pi$ and $\sigma$ are collections of subsets of a set $X$?

Published on 29 Mar 2026 - 5:44

score 81 · Answer 10 · 2026-03-29 07:29:11

81

Views

Prove that a numerical semigroup $S$ is symmetric if and only if it equals its canonical ideal.

Published on 29 Mar 2026 - 7:29

score 148 · Answer 11 · 2026-03-25 19:10:34

148

Views

Counterexamples to the Grothendieck group of a commutative monoid respecting tensor products

Published on 25 Mar 2026 - 19:10

score 421 · Answer 12 · 2026-03-29 05:49:49

421

Views

Explicit description of $\mathbb{Z}\otimes_{\mathbb{N}}\mathbb{Z}$

Published on 29 Mar 2026 - 5:49

score 44 · Answer 13 · 2021-08-05 18:54:38

44

Views

Terminology for semigroups where every element is a product

Published on 05 Aug 2021 - 18:54

score 632 · Answer 14 · 2026-03-29 05:49:57

632

Views

What does $\mathrm{Spec}(\mathbb{Z})\times_{\mathrm{Spec}(\mathbb{F}_{1})}\mathrm{Spec}(\mathbb{Z})$ look like?

Published on 29 Mar 2026 - 5:49

score 92 · Answer 15 · 2026-03-29 07:32:14

92

Views

Are affine binoid schemes equivalent to binoids? ($\mathbb{F}_{1}$-geometry)

Published on 29 Mar 2026 - 7:32

List Question

Why do $ \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}$ and $ \begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix}$ generate a free semigroup?

Is there a compact set $S$ in topological semigroup $T$ with $t^{-1}K\subseteq S$, where $K$ is compact set in $T$?

What type of property for subsemigroups or submonoids is this?

Cartesian product of finitely generated integral monoids

$|F\cap K^{-1}A|\leq \sum_{k\in K}|F\cap k^{-1}A|$?, where $K$ is compact set, $F$ is finite set in topological semigroup $T$

Markov chain semigroup: action on densities

Second isomorphism theorem for semigroups

First isomorphism theorem for inverse semigroups together with v-prehomomorphisms?

Is there a standard notation for the collection $\{R\cap S:R\in\pi,S\in\sigma\}$ where $\pi$ and $\sigma$ are collections of subsets of a set $X$?

Prove that a numerical semigroup $S$ is symmetric if and only if it equals its canonical ideal.

Counterexamples to the Grothendieck group of a commutative monoid respecting tensor products

Explicit description of $\mathbb{Z}\otimes_{\mathbb{N}}\mathbb{Z}$

Terminology for semigroups where every element is a product

What does $\mathrm{Spec}(\mathbb{Z})\times_{\mathrm{Spec}(\mathbb{F}_{1})}\mathrm{Spec}(\mathbb{Z})$ look like?

Are affine binoid schemes equivalent to binoids? ($\mathbb{F}_{1}$-geometry)

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