All Questions
Tagged with magma terminology
9
questions
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82
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Nomenclature for a unital magma together with a monoid
Is there some established name/nomenclature for structures $\mathfrak{A} = (A,\, {\oplus},\, {\odot})$, where
$(A,\, {\oplus})$ forms a (commutative) unital magma (in particular not associative!),
$(...
- 281
2
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2
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199
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What is the name for a magma which is neither a quasigroup nor a semigroup yet has both an identity and inverses?
Is there a name which is more specific than `unital magma' for a magma whose only requirements are that it should have both an identity and (L/R symmetric) inverses for all elements?
The following ...
- 407
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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 ...
- 68.1k
5
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199
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Terminology: Semigroups, only their "binary operations" aren't closed.
Motivation:
Consider $\mathcal{X}=(X, +)$, where $X=\{-1, 0, 1\}$ and $+$ is standard addition. Then $\mathcal{X}$ is associative (where defined) but not closed.
NB: There is an identity element in $X$...
- 45.8k
3
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1
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Name for the property of “being a Cartesian product of arbitrary sets”
Suppose I have a set $S$ of pairs (or, in general, tuples, or objects with two or more parts/attributes/projections). This set may have the property that
$$(a, b) \in S \wedge (a', b') \in S \...
- 988
2
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1
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145
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Is there a term for this property of magmas?
There exists an element of the magma c such that for all x: $ x*x=c $
The consequence of this is that the elements on the diagonal of the Cayley table are all the same, e.a:
$ * = \begin{bmatrix} 1 &...
- 3,285
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Is there a term for an algebraic structure with two binary operators that are closed under a set?
For example, let's say we're using the operators +, and *, and the set {0,1,2}
The Cayley tables look like this:
...
- 3,285
1
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2
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139
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Is there a standard name for a set equipped only with an idempotent binary operation?
Is there a name for an idempotent magma, or do they not arise often enough to warrant a special name?
(By idempotent binary operation, I mean an operation $+$ such that $x + x = x$ for any $x$.)
- 150
5
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Is there a name for magmas with $[x+y]+[x'+y'] \equiv [x+x']+[y+y']$?
Is there a name for magmas (written additively) satsisfying the following identity? The square brackets have no particular signifance, but will hopefully promote readability in what follows. $$[x+y]+[...
- 68.1k