Question

If $(G, \cdot)$ is a monoid, then $(\mathcal{P}(G), \cup, \cdot)$is a ring

score 58 · Answer 1 · 2023-03-03 20:29:04

58

Views

If $(G, \cdot)$ is a monoid, then $(\mathcal{P}(G), \cup, \cdot)$is a ring

Published on 03 Mar 2023 - 20:29

score 31 · Answer 2 · 2023-03-05 11:53:51

31

Views

If $f$ is a epimorphism from the monoid $(X,⊕,x_0)$ to the monoid $(Y,⊗, y_1)$ then $f(x_0)=y_1$ and $f(x^{-1})=f(x)^{-1}$ provided $x^{-1}$ exists.

Published on 05 Mar 2023 - 11:53

score 26 · Answer 3 · 2023-03-14 06:09:48

26

Views

A monoid structure $$ on all of $\Bbb{Z}$ isomorphic to $A \Bbb{Z} + 1$ for some $A \neq 0,1$ is such that $\Bbb{Z}\Bbb{Z}$ has infinite complement.

Published on 14 Mar 2023 - 6:09

score 99 · Answer 4 · 2026-03-26 11:56:01

99

Views

Grothendieck group.

Published on 26 Mar 2026 - 11:56

score 44 · Answer 5 · 2023-03-18 19:06:33

Show that a semi-group (E,T) (I.e., with T associative) satisfying a certain property is a monoid (i.e., possesses a neutral element)

score 85 · Answer 6 · 2023-03-20 18:01:57

85

Views

If $N$ is a subset of a monoid $(M,\bot ,e)$ with identity element $\epsilon$ with respect $\bot$ then does the equality $\epsilon=e$ holds?

Published on 20 Mar 2023 - 18:01

score 44 · Answer 7 · 2026-03-25 07:40:32

44

Views

The free semiring on the Boolean monoid

Published on 25 Mar 2026 - 7:40

score 37 · Answer 8 · 2023-03-21 21:18:33

37

Views

Monoid with torsion elements

Published on 21 Mar 2023 - 21:18

score 55 · Answer 9 · 2023-03-22 22:27:10

55

Views

Why do symmetric monoidal structures have such a confusing name?

Published on 22 Mar 2023 - 22:27

score 113 · Answer 10 · 2026-03-25 11:24:34

113

Views

For an even multivector $A$, if the map $X\mapsto AX\tilde A$ preserves grade, must $A$ be a product of vectors?

Published on 25 Mar 2026 - 11:24

score 62 · Answer 11 · 2023-04-12 14:22:51

62

Views

Clarifications needed in an exercise about semilattice and abelian monoids in Arbib and Manes' text

Published on 12 Apr 2023 - 14:22

score 35 · Answer 12 · 2026-02-23 08:36:56

35

Views

Generalization of free magmas for nested structures

Published on 23 Feb 2026 - 8:36

score 100 · Answer 13 · 2023-04-12 21:07:31

100

Views

Grothendieck group of a monoid with zero

Published on 12 Apr 2023 - 21:07

score 81 · Answer 14 · 2023-04-27 15:09:46

81

Views

A monoid $M$ is $\omega$-presentable in the category $M$-$\mathbf{Set}$

Published on 27 Apr 2023 - 15:09

score 48 · Answer 15 · 2023-05-01 09:43:49

48

Views

Something similar to Kronecker basis theorem for semigroup

Published on 01 May 2023 - 9:43

List Question

If $(G, \cdot)$ is a monoid, then $(\mathcal{P}(G), \cup, \cdot)$is a ring

If $f$ is a epimorphism from the monoid $(X,⊕,x_0)$ to the monoid $(Y,⊗, y_1)$ then $f(x_0)=y_1$ and $f(x^{-1})=f(x)^{-1}$ provided $x^{-1}$ exists.

A monoid structure $$ on all of $\Bbb{Z}$ isomorphic to $A \Bbb{Z} + 1$ for some $A \neq 0,1$ is such that $\Bbb{Z}\Bbb{Z}$ has infinite complement.

Grothendieck group.

Show that a semi-group (E,T) (I.e., with T associative) satisfying a certain property is a monoid (i.e., possesses a neutral element)

If $N$ is a subset of a monoid $(M,\bot ,e)$ with identity element $\epsilon$ with respect $\bot$ then does the equality $\epsilon=e$ holds?

The free semiring on the Boolean monoid

Monoid with torsion elements

Why do symmetric monoidal structures have such a confusing name?

For an even multivector $A$, if the map $X\mapsto AX\tilde A$ preserves grade, must $A$ be a product of vectors?

Clarifications needed in an exercise about semilattice and abelian monoids in Arbib and Manes' text

Generalization of free magmas for nested structures

Grothendieck group of a monoid with zero

A monoid $M$ is $\omega$-presentable in the category $M$-$\mathbf{Set}$

Something similar to Kronecker basis theorem for semigroup

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