# 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.)

135 questions
Filter by
Sorted by
Tagged with
24 views

### Why to have an inverse element (for example taken from bijection definition) do we need start from an unital magma?

I pictured something like the set of the Real numbers, with “1” removed. Every number in the set has a multiplicative inverse, and the set lacks an identity element. One could start with axioms ...
44 views

### 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 ...
44 views

### “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 ...
34 views

### List of equations in MAGMA

I have some integer $n$, some ambient affine space $\mathbb{A}^n$, and a list $L$ of equations $f_{ij}$ cutting out a variety $X$ in the ambient space. I have problems defining the list $L$ correctly. ...
9 views

### How does one find functionally complete sets, or sole sufficient operators, on more than two truth values?

In standard two-valued logic, it is known that either NAND or NOR is sufficient by itself to construct all possible logic gates - all functions 2 × 2 → 2. But I've not been able to find anything about ...
31 views

### Direct decomposition of a magma onto ideals

Let's call the product of submagmas $A \cdot B$ a direct decomposition of a magma $M(\cdot)$ if: $A \cdot B = M$ ($m = a \cdot b$ for any element $m$ of $M$, where $a$ is an element of $A$ and $b$ is ...
34 views

23 views

### 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 ...
35 views

### 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 ...
28 views

### Generated submagma of a free magma

Let $X$ be a set and $S\subset X$. Let $M(X)$ denote the free magma constructed on $X$ and $i:S\hookrightarrow X$ be the canonical injection of $S$ into $X$. We know that there exists a unique ...
22 views

46 views

### All magmas of order n (specifically 3)

I am considering the collection of all magmas (sets with binary operations) of order 3. Since we just need a binary operation and no other properties, it makes sense to define a magma in terms of all ...
39 views

89 views

### Given an algebra structure $(X,*)$ s.t. $(x*y)*y = y*(y*x) = x$ , prove$x*y=y*x$.

Suppose $(X,*)$ is arbitrary algebraic structure such that $\forall x,y\in X$, we have $(x*y)*y = y*(y*x) = x$, prove that $x*y=y*x$. This question seems pretty simple but I tried and I failed.
133 views

### Commutative subtraction

It is well known that subtraction is not commutative in general. However, it is commutative in some groups: $\mathbb I$, $\mathbb C_2$, $\mathbb K_4$. I am trying to understand the logic. ...
45 views

### How many magmas exist on $n$-element set

It is clear that we can make $n^{n^2}$ Latin squares (I think that this is no real Latin square, but I don't know how to name it) for $n$-element set, but I have heard that some magmas will be ...
60 views

### Elements $A\in GL_4(\mathbb{Z}_2)$ with $A^5=I, A\neq I$ by using GAP.

I need elements $A\in GL_4(\mathbb{Z}_2)$(General linear group of $4\times 4$ matrices over $\mathbb{Z}_2$ ) with $A^5=I, A\neq I.$ By using simple calculation its hard to find such types of elements....
64 views

### Have a magma structure when “if the set of integers with respect to subtraction is not a group”? [closed]

I have a 3 answers but nobody return me a mathematical structure/category name when I try to classify "the set of integers with respect to subtraction is not a group" 1) Subtraction of integers (and ...
226 views

### Magma function for modulo irreducible polynomial

So, I am trying to make a program in Magma which returns the value table of a given function F over a field $GF(2^n)$. To do so I need a irreducible polyomial. For example, I've considered $GF(2^3)$ ...
29 views

### Invertibility as Criteria for a Loop

I try to understand the correct criteria for a Loop. I see in Wikipedia https://en.wikipedia.org/wiki/Inverse_element#In_a_unital_magma that “A unital magma in which all elements are invertible is ...
68 views

### Generating subsets of a finite magma

I am trying to write a program which, given a multiplication table of a finite magma $(G, *)$, should produce at least one (or all possible) generating subset $S$ of minimal cardinality. More ...
65 views

### Question related to Magma

I am reading some notes in which I found the following exercise: Suppose $G$ is a magma then $G$ is associative and satisfy cancellation properties. I think this is not true for instance matrix ...
190 views

### Notions of basis and span in a magma

Suppose that $C$ is a set with closure under the binary operation $+$. $(C,+)$ is therefore a magma. I am trying to figure out if notions of basis, or span make sense in a magma. Spanning set (?) ...
70 views

### Prove that there is no bijective homomorphism from $\left(\mathbb{Q},\ +\right)$ to $\left(\mathbb{Q_+^*},\ \times \right)$

I need to prove that there does not exist any bijective homomorphism from $\left(\mathbb{Q},\ +\right)$ to $\left(\mathbb{Q_+^*},\ \times \right)$ Here is a way to prove it: Let $f$ be a ...