All Questions
Tagged with magma reference-request
7
questions
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Compilation of Phenomena Modeled by an Operation Table
It seems like there would be utility in a search engine or database through which the user inputs the operation table of a magma (I think that's the right level of algebraic structural generality) to ...
- 1,922
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Generalization of free magmas for nested structures
Consider a nonempty set $X$. What is the name / concept that gives rise to (the set of) all $X$ labeled planar trees e.g.
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- 20.4k
3
votes
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answer
394
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Does this notion of "weak" isomorphism exist in literature?
Let $(M,\circ)$ and $(N,\ast)$ be two magmas.
I'd like to relax the notion of isomorphism by defining a notion of "weak" isomorphism in the following way:
$M$ and $N$ are "weakly" isomorphic if there ...
- 3,386
3
votes
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208
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Referencing the construction of a left loop
We call left loop a magma $(L,\cdot)$ such that
for all $(a,b)\in L\times L$, exists only one $x\in L$ such that $a\cdot x=b$,
exists one $e\in L$ such that $e\cdot x=x=x\cdot e$ for all $x\in L$.
...
- 3,396
2
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Functions $h$ such that $h(x*x') = f(x) * g(x').$
Definition 0. Call a magma $X$ surjective iff the distinguished binary operation of $X$ induces a surjective function $X \times X \rightarrow X$.
Now for the main idea:
Definition 1. Let:
$...
- 68.1k
3
votes
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Generalization of prime and irreducible elements to arbitary magmas
Has anyone ever given a general definition of prime and irreducible elements in arbitrary magmas, that is to say, sets with a single binary operation with no restrictions? I know Walter Noll has given ...
- 21.5k
9
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What can we learn about a magma by studying these monoids?
Given a magma $(X,*)$, we get three monoids in the following way. First, define a pair of functions $L,R : X \rightarrow (X \rightarrow X).$
$$(Lx)(y) = x*y,\quad (Rx)(y) = y*x$$
Then each of the ...
- 68.1k