All Questions
Tagged with semigroups-and-monoids ra.rings-and-algebras
113 questions
5
votes
2
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537
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If $k[S]$ is noetherian, is S finitely generated?
Let $S$ be a semigroup. If $S$ is abelian, then it follows that the semigroup algebra $k[S]$ is finitely generated if and only if $S$ is.
What if we relax the condition on $k[S]$, so that $k[S]$ is ...
- 11.6k
0
votes
1
answer
403
views
When does a power semigroup have a zero, and what can the zero be?
Let $S$ be a semigroup. The power semigroup of $S$ is the set $P(S)=2^S\setminus\lbrace\varnothing\rbrace $ with the operation $$AB=\lbrace ab\ |\ a\in A,\ b\in B\rbrace.$$
This operation is ...
- 1,445
1
vote
2
answers
442
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submonoids of Z_n
Anyone knows how to describe explicitly the submonoids of Z_n, regarded as a multiplicative
monoid?
2
votes
0
answers
51
views
Existence of a canonical embedding from a quotient of $\mathscr{F}^\ast(\mathcal A(H))$ to another
Let $H$ be a multiplicative, commutative monoid, and denote by $H^\times$ the group of units of $H$, by $\mathcal A(H)$ the set of atoms (or irreducible elements) of $H$, by $\mathscr{F}^\ast(\mathcal ...
- 10.5k
3
votes
1
answer
297
views
Is the universal inverse semigroup of a commutative semigroup an embedding?
The question of existence of a universal inverse semigroup of an arbitrary semigroup has been answered before (this is a construction similar to the Grothendieck group). Let's refer to the universal ...
- 2,464
3
votes
1
answer
243
views
Embedding Semigroups in Rings
Let $S$ be a finite commutative semigroup with identity. Under what conditions (on the semigroup $S$) it is possible to find a ring $R$ such that the multiplicative structure of $R - \{0\}$ is ...
- 801
2
votes
1
answer
290
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Idempotents in Green J classes
I recently read this article Syntactic semigroups. In page $8$, he speaks about a J class having an idempotent is called regular:
A $\mathcal J$-class containing an idempotent is called regular. ...
- 233
4
votes
2
answers
607
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Invertible elements in monoid rings of unital monoids without non-trivial invertible elements
This question is somewhat related to Tilmans notorious problem in this post. Let $(M,\cdot)$ be a monoid with unit $1$ and set
$$(M,\cdot)^{\times} := \lbrace x \in M \mid \exists y \in M : xy=yx=1 \...
- 25.5k
3
votes
0
answers
126
views
dual composition of binary relations
I'm not sure if this is of any interest at all, but I spent some time looking at it a couple of years ago so I'd like to ask for input on this.
Given two binary relations $\rho,\,\sigma$ on a set $X,$...
- 1,445
0
votes
1
answer
128
views
What are the semigroups in which congruence classes can be multplied like sets?
For a semigroup $S$ and a congruence $\rho$ on $S$, let's say that $\rho$ is good when for all $a,b\in S$ we have that $[ab]=[a][b],$ where $[x]$ denotes the congruence class of $x$ modulo $\rho$ and ...
- 1,445
2
votes
1
answer
1k
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monoid ring and some structure within it - how is it called?
I am amateur - mathematics is my hobby, and I find some strange structure working with toy matrices structure so I try to ask some questions regarding it. Let me allow to introduce some structure ...
- 1,626
1
vote
2
answers
394
views
Relations in matrix semigroups
Suppose that $A_1, \dots, A_k \in M_n(\mathbb{Q})$ and $S$ is the semigroup generated by them. Two questions: are there always a finite set of relations $\{R_i\}$ among the $A_j$ such that $S$ is ...
- 4,636
0
votes
0
answers
72
views
Decomposition results for locally commutative semigroups
Every finite abelian group is the direct product of its cyclic groups of prime order, and every commutative monoid divides a product of its cyclic submonoids. Could these results generalized to ...
- 798