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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When do we have $(x y)^2 = x^2 y^2 $?
I just started thinking about algebra so this might be a trivial question.
Anyway,
Under what conditions do we have
$$(x y)^2 = x^2 y^2 $$ ?
Does it need to be a group ?
Or a groupoid ?
Or a monoid ?
...
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Computing the number of conjugacy-classes in $GL_{n}(\mathbb{F}_{p})$ of elementary abelian p-subgroups by GAP and Magma
I'm trying to compute the number of conjugacy-classes of elementary abelian p-subgroups of rank $2$ in $GL_{n}(\mathbb{F}_{p})$ by GAP and Magma. So I consider the following GAP function:
...
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Is every group isomorphic to the automorphism group of some magma?
I believe that magma isomorphism is defined as $\phi(x*y)=\phi(x)*'\phi(y)$. The automorphism group is the set of bijective isomorphisms from the elements of the magma to itself, under the operation ...
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What's the preferred term researchers like to use in the theory of magmas/groupoids?
As we know, mathematicians like to avoid the term "groupoid" to refer to a set with binary operation. This term, as we know, originates from the works of Brandt, so called Brandt groupoid. A ...
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Is there a category of partially defined binary operations?
A magma is a set $Y$ with a binary operation $m:Y \times Y \rightarrow Y.$ A partial magma is the same idea, but where the binary operation $m$ may not be defined on some pairs of elements of $Y.$ My ...
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If not associative, then what?
Consider a binary operation $*$ acting from a set $X$ to itself. It's useful and standard to work with operations which are associative, such that $(a*b)*c = a*(b*c)$. What about operations which are ...
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Fill in a partly filled in table such that it makes the magma $(M,*)$ associative, commutative, has an identity element and has no zero-elements.
Below is a partly filled in table for a binary operation ($*$) on the set $M=\{a,b,c,d\}$. I am trying to fill in the rest such that the magma $(M,*)$ becomes associative, commutative, has an identity ...
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Are all alternative magmas flexible?
A magma is alternative if for all elements $x$ and $y$, we have $(xx)y = x(xy)$ and $y(xx) = (yx)x$. A magma is flexible if for all elements $x$ and $y$ we have $x(yx) = (xy)x$. Both of these are ...
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Power associative magma
I’m looking for a magma with specific properties:
Requirements:
1.Power Associative(of course, I want it to not be alternative or similar).
2.Invertibility and identity element.
Preferences(In order ...
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"Equivalence relation compatible w/magma law" in Bourbaki's Algebra I
I am using the edition of Bourbaki's "Algebra I" published/printed by Springer in 1989. On p. 11 Bourbaki defines the compatibility between a magma law ⊤ and an equivalence relation R on the ...
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Notation and terminology for free algebras with one binary operation?
Introduction To Question
Context: Universal Algebra
I
Definition: A $\mathtt{S}$-algebra is an algebra $\langle A, succ, \bullet \rangle, $ with one unary operation and no identities.
Let $\mathsf{S}(...
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Is totally ordered magma infinite?
It is well known that any non-trivial totally ordered group is infinite.
Is it true that any totally ordered magma with more than one element is infinite too?
My attempt to prove the statement:
Let'...
- 1,120
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Principal ideal of a non-associative magma
The definitions of a left, right, and two-sided ideal of an algebra do not involve associativity
(R.D. Schafer "An Introduction To Nonassociative Algebras").
The same we can say about the definitions ...
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How to construct a free magma without using identifications/disjoint union?
Let $S$ be a set. We define a sequence of sets
$(S_n)_{n\in\mathbb{N}^*}$ recursively as follows: $S_1=S$ and for
$n\ge2$ $$S_n=\bigcup_{k=1}^{n-1}\{k\}\times\big(S_k\times
S_{n-k}\big).$$ Let $...
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Every submagma of a free magma is free
Let $X$ be a set. Let $M_X$ be the free magma constructed on $X$.
Suppose $N\subset M_X$ is a submagma of $M_X$: i.e. $NN\subset N$. Let $u:(N-NN)\rightarrow N$ be the canonical injection. We know ...
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