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Tagged with magma idempotents
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Conservative idempotent magma - proof attempt
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 ...
5
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What is difference between idempotent magma and unital magma?
I don't understand well in what way idempotent element is wired to identity element in a magma context.
idempotent: $x \cdot x = x$
identity element: $1 \cdot x = x = x \cdot 1$
For example ...
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answer
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Idempotent that isn't any of these
Let $A=\left\{x,y,z\right\}$ and $M=\left\{g\mid g:A\rightarrow A\text{ is a function}\right\}$.
Is there an element in $M$ that is idempotent but not right absorbing, left absorbing, a right ...
user281997
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2
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Is there a standard name for a set equipped only with an idempotent binary operation?
Is there a name for an idempotent magma, or do they not arise often enough to warrant a special name?
(By idempotent binary operation, I mean an operation $+$ such that $x + x = x$ for any $x$.)
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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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