All Questions
14
questions
0
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82
views
Nomenclature for a unital magma together with a monoid
Is there some established name/nomenclature for structures $\mathfrak{A} = (A,\, {\oplus},\, {\odot})$, where
$(A,\, {\oplus})$ forms a (commutative) unital magma (in particular not associative!),
$(...
- 281
0
votes
0
answers
36
views
Generalization of free magmas for nested structures
Consider a nonempty set $X$. What is the name / concept that gives rise to (the set of) all $X$ labeled planar trees e.g.
...
- 20.4k
3
votes
2
answers
169
views
How many non-isomorphic algebraic structures (i.e. magmas, monoids, groups etc.) are there with countably infinite order? [closed]
For structures of finite order it seems obvious to me that there are countably infinite in total, by a simple diagonalization argument (starting at all of order 1, then 2 etc.). It is however not ...
- 462
5
votes
2
answers
498
views
Good book for self-study of Magmas/Semigroups/etc.?
I'm currently an undergrad in my second semester of Abstract Algebra. We've covered groups, rings, fields, all that fun stuff. I'm working with Shahriari's "Algebra in Action" as well as ...
1
vote
1
answer
2k
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What is a monoid in simple terms?
I encountered the term "monoid" but I didn't really understand what is it useful for or what's it about.
If I understand correctly a "monoid" is something defined in the context of ...
- 1,609
5
votes
0
answers
204
views
Suspicious diagrams on wiki about group-like structures
It seems to me that the diagrams on wiki about group-like structures are not quite right. For example, the following
https://en.wikipedia.org/wiki/Monoid#/media/File:Algebraic_structures_-...
- 274
3
votes
0
answers
49
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Each magma $M$ is associated with monoids $\mathcal{L}(M)$ and $\mathcal{R}(M)$. What are these called, and have they been studied?
Let $X$ denote a magma. Then $\mathrm{List}(X)$ is a monoid equipped with both a left and a right action on $X$, where the actions are defined in the obvious way. To illustrate these actions, suppose ...
- 68.1k
3
votes
7
answers
122
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Is $G = (\Bbb Q^*,a*b=\frac{a+b}{2})$ a group, monoid, semigroup or none of these?
Is $G = (\Bbb Q^*,a*b=\frac{a+b}{2})$ a group, monoid, semigroup or none of these?
I tried to solve it by assuming $ a,b,c \in G $ such that $a*(b*c)=(a*b)*c$. Then$$\frac{a+\frac{b+c}{2}}{2} = \frac{...
- 189
1
vote
1
answer
51
views
Is the Binary Operation ever Invertible in a Semigroup?
A semigroup is a set $S$ together with an associative binary operation $m:S\times S\rightarrow S$.
In any kind of semigroup I can think of (group, ring, field, etc), this binary operation $m$ is not ...
- 7,789
4
votes
1
answer
349
views
Is there a name for an algebraic structure with only "addition" and "truncated subtraction"?
Given a set $S$ with
An associative binary "addition" operation $+$ with corresponding neutral element $0$ such that $(S, +)$ is a monoid
A non-associative binary "truncated subtraction" operation $-$...
- 1,145
2
votes
1
answer
456
views
In the coproduct of monoids $A\amalg B$, suppose two words have the same suffix in $B$. Can it be cancelled?
Let $A,B$ be monoids and $A\amalg B$ their product in the category of monoids, comprised of reduced words. Previously I have asked about the canonical arrow $A\amalg B\to A\times B$ given by e.g $$...
- 14k
4
votes
1
answer
387
views
Elegant approach to coproducts of monoids and magmas - does everything work without units?
From this answer by Martin Brandenburg I learned an elegant way of constructing and describing elements of coproducts of monoids. There he writes this construction shows the existence of colimits in ...
- 14k
5
votes
2
answers
862
views
Is a monoid a magma?
According to this wikipedia page, a monoid is defined as an object that contains
An associative binary operation
An identity element
There is no mention of the object necessarily containing a set.
...
- 181
6
votes
3
answers
621
views
Is there a name for an element $z$ such that $\,zx = z = xz\,$ for all $x$?
Is there a general name for the following properties, (similar to the properties of existence of an additive identity, existence of multiplicative identity etc):
For any given set, the intersection ...
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