Questions tagged [magma]

Question 1

I am exploring a particular algebraic structure defined as follows: Let $(M, ∗)$ be a set $M$ equipped with a binary operation such that: $*$ is commutative: $a * b = b * a$ for all $a, b \in M$. ...

Question 2

Let $E/\mathbb{Q}: y^2=x^3+ax+b$ be an elliptic curve with $E(\mathbb{Q})[2]\cong \mathbb{Z}/2\mathbb{Z}$. I know that we can rewrite the equation of $E/\mathbb{Q}$ in the form $y^2=x^3+a'x^2+b'x$ (...

Question 3

Is there a term in use (ever used?--I have not had much luck in my attempts at literature review) to designate an algebraic structure with two operations, one of which satisfies the properties of a ...

Question 4

Let $A$ be a quiver algebra (with admissible relations) of finite global dimension and $M$ a finite dimensional basic $A$-module. Is there a way to use a computer algebra system like Magma to ...

Question 5

Let $K$ be a cyclotomic field defined in MAGMA, via K:=CyclotomicField(N). Let $x$ be an element in $K$ that is not contained in $\mathbb{Q}$. I try to run the ...

Question 6

I am working through Will Steins Math129 course, some of which requires the use of MAGMA. Specifically, assignment two (question 2a) requires the factorization of the ideal (2004) over the Gaussian ...

Question 7

I have been investigating commutative, associative magmas in an ad hoc way for the past few days and was curious about idempontent-free magmas. The magma $(\mathbb{Z}_{\ge 1}, +)$ is idempotent-free, ...

Question 8

I know there exist non-empty magmas $(S;*)$ which are both completely non-associative and non-commutative (completely non-commutative means $x*y \neq y*x$ unless $x=y$, and completely non-associative ...

Question 9

Let $k \in \mathbb{N^*}$ and $r$ a divisor of $k$. Then : $$M_{k,\ r}=\{k,\ k+r,\ k+2r,\ k+3r,\ \cdots\}$$ is a collection of proper semi-group of $\mathbb{N}$ for $+$ (classic addition), which are ...

Question 10

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 ...

Question 11

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\...

Question 12

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: ...

Question 13

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)...

Question 14

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, ...

Question 15

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 ...

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Questions tagged [magma]

Is the variety defined by $x(yz) = (xz)y$ (in commutative unital magmas) known or studied?

Elliptic curve $y^2=x^3+ax^3+bx$ with rational 2-torsion in Magma/Sage

What do you call a structure such that its group operation distributes over the operation under which it is a commutative magma?

Calculating the Ext algebra of a module via magma

Coercion between a number field and a cyclotomic field in MAGMA

MAGMA returning non-principal ideals when factorizing primes over a ring of integers in a PID

Alternative proof that a power-associative magma with no idempotent elements is infinite.

Is there a magma with at least 2 elements which is commutative but almost completely non-associative?

Collection of not-numerical semi-group of $\mathbb{N}$

Conservative idempotent magma - proof attempt

Weaker notion of closure for partial magmas

map from spin to special orthogonal in Magma [closed]

Practical example of differences between associativity and alternativity (and the in-between Bol loop)? [closed]

Smallest possible cardinality of finite set with two non-elementarily equivalent magmas which satisfy the same $\forall$-theory?

Are there 45 unital magmas with three elements (up to isomorphism)?

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