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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Are there interesting examples of medial non-commutative semigroups?
There exist semigroups $S$ (written additively) such that
$S$ is medial, meaning $(a+b)+(a'+b') = (a+a')+(b+b')$.
$S$ is not commutative.
Example. The left (and right) zero semigroups are all medial,...
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A question on certain "magma" structures
Let $S$ be a non-empty set and $*$ be a binary operation on $S$ such that the following axioms hold:
for every $x,y,z∈S$ , $x*(y*z)=(x*z)*y$;
$(S,*)$ has a right identity i.e. there exists $e∈S$ such ...
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Is there a name for magmas with $[x+y]+[x'+y'] \equiv [x+x']+[y+y']$?
Is there a name for magmas (written additively) satsisfying the following identity? The square brackets have no particular signifance, but will hopefully promote readability in what follows. $$[x+y]+[...
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Proper term for a monotonic magma
Let $M$ be the multiplication table for a finite magma. Entries are labeled $0,\ldots,n-1$.
M has the property that $M(i,j)\ge i, M(i,j) \ge j$.
What is the proper term for this kind of magma and ...
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What is this algebraic object called?
I was playing around with the following object: Let $Q$ be a set with a binary operator $\cdot$ obeying the axioms:
$a \cdot a = a$ (idempotence)
$a \cdot (b \cdot c) = (a \cdot b) \cdot (a \cdot c)$ ...
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Discuss whether or not the following binary operations are commutative, associative, ...
Discuss whether or not the following binary operations are commutative, associtive, have neutral elements and for which elements there are inverse elements.
In between are what I have said, but if it ...
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prove no identity element in the given Cayley Table of three elements
Prove that the operation in the following Cayley table has no identity element:
$$
\begin{array}{c|ccc}
\hline
* & u & v & w \\
\hline
u & u & w & w \\
v & v & v & ...
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How are the powers being changed
I have a semigroup $S$ including a generator, say $d$, such that $$d^4=d$$ I am trying to guess the general rule of $d$'s powers such that when I want to calculate $d^n, n\in\mathbb N$; I can simplify ...
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Inverse elements in the absence of identities/associativity.
Lets view groups as consisting of a binary operation, a distinguished element $e$, and unary operation $x \mapsto x^{-1}$. Then the group axioms can be stated as follows.
$(xy)z=x(yz).$
$xe=ex=x.$
$...
- 68.1k
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Which properties are inherited by the Cartesian product of two sets equipped with a binary operation?
Let $G$ and $H$ denote sets equipped with a binary operation (aka magmas). We can form the Cartesian product magma $G \times H$ in the obvious way. I'm interested in which properties of $G$ and $H$ ...
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Left continuous magmas with no fixed points
Let $X$ be a compact Hausdorff topological space, and $*: X^2\rightarrow X$ an associative map (so that $(X, *)$ is a semigroup) which is left continuous (for all $s\in X$, the map $t\mapsto ts$ is ...
- 249k
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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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Prove this magma commutativity
Given magma $(X, *)$ and that $(x*y)*y = x$ and $y*(y*x) = x$ $\forall x, y \in X$ prove that $x*y = y*x$.
Should be rather simple but I've been trying to prove that for several hours now with no ...
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A finite, cancellative semigroup is a group
Let $G$ be a finite, nonempty set with an operation $*$ such that
$G$ is closed under $*$ and $*$ is associative
Given $a,b,c \in G$ with $a*b=a*c$, then $b=c$.
Given $a,b,c \in G$ with $b*a=c*a$, ...
user39794
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Is there an easy way to see associativity or non-associativity from an operation's table?
Most properties of a single binary operation can be easily read of from the operation's table. For example, given
$$\begin{array}{c|ccccc}
\cdot & a & b & c & d & e\\\hline
a &...
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