Question

Semigroups (ideals of a semigroup)

score 184 · Answer 1 · 2013-10-16 05:05:22

184

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Semigroups (ideals of a semigroup)

Published on 16 Oct 2013 - 5:05

score 77 · Answer 2 · 2013-10-20 23:03:09

77

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What operations is this set closed under? The set of all $\{(a,b) : (a,b) \in \Bbb{Z}^2, \gcd(a,b) \neq 1\}$.

Published on 20 Oct 2013 - 23:03

score 74 · Answer 3 · 2013-10-23 03:07:41

74

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Can we say anything about the structure of the semigroup of non-coprime pairs after this?

Published on 23 Oct 2013 - 3:07

score 116 · Answer 4 · 2013-10-23 06:16:19

116

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Proof of Green's Relation

Published on 23 Oct 2013 - 6:16

score 459 · Answer 5 · 2013-11-04 03:06:36

459

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definition of (semi)group (co)homology

Published on 04 Nov 2013 - 3:06

score 144 · Answer 6 · 2013-11-04 23:41:56

144

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If $S$ is a right group, then every $\mathcal L$-class is a $\mathcal H$-class and also a subgroup.

Published on 04 Nov 2013 - 23:41

score 78 · Answer 7 · 2013-11-05 11:41:13

78

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Does there exist a commutative magma such that $\mid$ is transitive, which is not a semigroup?

Published on 05 Nov 2013 - 11:41

score 271 · Answer 8 · 2026-03-25 06:13:11

271

Views

Is the set of all uniquely invertible elements of a semigroup an inverse subsemigroup?

Published on 25 Mar 2026 - 6:13

score 123 · Answer 9 · 2026-03-25 22:04:40

123

Views

Necessary and sufficient conditions for the embeddability of a semigroup in a group

Published on 25 Mar 2026 - 22:04

score 140 · Answer 10 · 2013-11-15 17:56:32

140

Views

A semigroup $S$ that $|S| > 2$ is regular if and only if $x^2=x$ for any $x \in S$ where $S-\{x\}$ is a group

Published on 15 Nov 2013 - 17:56

score 235 · Answer 11 · 2013-11-17 08:08:10

235

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Why do the interesting antihomomorphisms tend to be involutions?

Published on 17 Nov 2013 - 8:08

score 32 · Answer 12 · 2013-11-19 17:37:06

Does there exist a semigroup such that every element factorizes in this way, which nonetheless lacks a left identity?

score 230 · Answer 13 · 2013-11-20 07:07:11

Does there exist a semigroup such that $(xy)^n = x^n y^n$ that is non-Abelian? If so, can this property be finitely axiomatized?

score 146 · Answer 14 · 2013-11-21 19:09:05

146

Views

If $S$ is a finitely generated periodic semigroup with the permutation property, then $S$ is finite.

Published on 21 Nov 2013 - 19:09

score 445 · Answer 15 · 2026-03-27 21:35:49

445

Views

On the powerset of a monoid, does the second operation play nice with the first? Indeed, is it even useful?

Published on 27 Mar 2026 - 21:35

List Question

Semigroups (ideals of a semigroup)

What operations is this set closed under? The set of all $\{(a,b) : (a,b) \in \Bbb{Z}^2, \gcd(a,b) \neq 1\}$.

Can we say anything about the structure of the semigroup of non-coprime pairs after this?

Proof of Green's Relation

definition of (semi)group (co)homology

If $S$ is a right group, then every $\mathcal L$-class is a $\mathcal H$-class and also a subgroup.

Does there exist a commutative magma such that $\mid$ is transitive, which is not a semigroup?

Is the set of all uniquely invertible elements of a semigroup an inverse subsemigroup?

Necessary and sufficient conditions for the embeddability of a semigroup in a group

A semigroup $S$ that $|S| > 2$ is regular if and only if $x^2=x$ for any $x \in S$ where $S-\{x\}$ is a group

Why do the interesting antihomomorphisms tend to be involutions?

Does there exist a semigroup such that every element factorizes in this way, which nonetheless lacks a left identity?

Does there exist a semigroup such that $(xy)^n = x^n y^n$ that is non-Abelian? If so, can this property be finitely axiomatized?

If $S$ is a finitely generated periodic semigroup with the permutation property, then $S$ is finite.

On the powerset of a monoid, does the second operation play nice with the first? Indeed, is it even useful?

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