Questions tagged [magma]
A magma is a set together with a binary operation on this set. (For questions about the computer algebra system named Magma, use the [magma-cas] tag instead.)
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Conservative idempotent magma - proof attempt
I need help with checking proof about idempotent and conservative magmas.
Let magma be any ordered pair $(M, \odot)$, where $M$ is nonempty set and $\odot$ binary operation on $M$.
Now I need to ...
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Is subtraction on the reals isomorphic to division on the positive reals?
I know that the magma $(\mathbb{R};+)$ of addition on the real numbers is isomorphic to the magma $(\mathbb{R}^+;\times)$ of multiplication on the strictly positive real numbers. I wonder, is it the ...
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Weaker notion of closure for partial magmas
Let $(G,\cdot)$ be a partial magma (a set endowed with a partial binary operation). In principle, for such generic structures it is possible that $\exists g \in G$ such that $\forall h \in G, \, g\...
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map from spin to special orthogonal in Magma [closed]
Let $G:=\operatorname{Spin}(7,5)$. How to construct in Magma the map $G \rightarrow G/Z(G) $ where $Z(G)$ is the center. I get this from Magma:
...
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Practical example of differences between associativity and alternativity (and the in-between Bol loop)? [closed]
Associativity is:
$$(a * b) * c = a * (b * c)$$
Alternativity is:
$$a * (a * b) = (a * a) * b$$
$$(a * b) * b = a * (b * b)$$
Bol loop is:
$${\displaystyle a(b(ac))=(a(ba))c}$$
$${\displaystyle ((ca)b)...
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Smallest possible cardinality of finite set with two non-elementarily equivalent magmas which satisfy the same $\forall$-theory?
This is a follow-up to my previous question, here: Smallest possible cardinality of finite set with two non-elementarily equivalent magmas which satisfy the same quasi-equations?. My question now is, ...
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Are there 45 unital magmas with three elements (up to isomorphism)?
How many unital magmas (magma with an identity element) with three elements are there (up to isomorphism)?
My approach:
List out all of the possible 2x2 multiplication tables for the two non-identity ...
- 12.7k
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5
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Why did I never learn about magmas?
While I’ve never taken an actual abstract algebra course, there are some things I know about the typical curriculum structure:
First, define an algebraic structure.
Explain groups.
Everything else.
...
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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!),
$(...
- 40.8k
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Associativity test for a magma
Say I have the operation table for a magma. I want to know whether or not the operation is associative. However, associativity is defined for an operation on 3 elements, and the operation table deals ...
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Inverse element of a magma
It is accepted that two elements are inverse to each other if their product is equal to the identity element:
Inverse element in a magma
https://en.wikipedia.org/wiki/Inverse_element
The definition ...
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Maximal Extension Chain of Halfgroupoids
A book I am reading gives the following definitions:
A collection $\{L_i:i=0,1,2,...\}$ of halfgroupoids $L_i$ is called an extension chain if $L_{i+1}$ is an extension of $L_i$ for each $i$. If $G$ ...
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Closest Equivalent to Cayley Graphs for Partial Groupoids?
[A partial groupoid (half-magma) is a set S equipped with a (single-valued) partial binary operation, as in Bruck's Survey of Binary Systems.]
This question may be nonsensical, given that the duality ...
- 31
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Does 2nd power idempotency imply all nth powers idempotency?
Suppose $(M,*)$ is a magma, that is, just a set with a binary operation with no conditions imposed, and let $s$ be an element of $M$. Also, let $n$ be an integer greater than or equal to $2$. An $n$-...
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Does there exist a magma where every element has a left cube root but not every element has a right cube root?
Let $(M,*)$ be a magma. $x$ is said to be a left cube root of $y$ if $(x*x)*x=y$. $x$ is said to be a right cube root of $y$ if $x*(x*x)=y$. Does there exist a magma where every element has a left ...
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