All Questions
Tagged with magma examples-counterexamples
8
questions
2
votes
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answers
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Groupoid with division
I'm searching an example of a grupoid with division which is not a quasigroup. A grupoid $(G, \cdot)$ is with division if $a\cdot G=G\cdot a=G$. I was thinking to try $(\mathbb{Q},\cdot)$, where $x\...
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4
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Examples of magmas with all their elements idempotents
A magma is supposed to be closed under a binary operation. Are there examples of magmas with all their elements idempotents under the operation of the magma?
16
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6
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Just How Strong is Associativity?
A friend of mine is using a lot of algebra that is not associative for an advanced Chemistry project. We were discussing it recently and I found it rather amusing how often she said things like "...
- 45.8k
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votes
1
answer
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specific magma examples
Give an example of a magma $S$ such that $S$ has a zero and $S$ has a left zero divisor that is not a right zero divisor
an example of a magma with an identity such that there is an element with ...
- 621
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Can an algebraic structure such that $x+a=x+b$, have solutions for all $a,b∈\mathbb{K}$ exist?
Does there exist an algebraic structure $(\mathbb{K},+)$ such that equations of the form $x+a=x+b$, $a\neq b$ have solutions for all $a,b\in \mathbb{K}$?
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55
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answers
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Can you give me some concrete examples of magmas?
I've seen the following (e.g. here):
I've learned a bit about groups and I could give examples of groups, but when reading the given table, I couldn't imagine of what a magma would be. It has no ...
- 24.2k
5
votes
1
answer
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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,...
- 68.1k
4
votes
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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 ...
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