Materials about Non-unital Idempotent Magmas? I'm a…
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Materials about Non-unital Idempotent Magmas?
I'm a hobbyist in math, so I mostly only know things that I could learn on youtube and the limited amount of info I could learn from wikipedia.
I'm really interested in learning more about magmas where there's no identity element, and every element is idempotent.
I've played around with linear combinations of a magma consisting of
\* | i | j | k
-|-|-|-
**i** | i | k | -j
**j** | -k | j | i
**k** | j | -i | k
so: [; m = ai + bj + ck; a,b,c ∈ ℝ ;]
And I think I figured out that most of these *m* have and element *q*, such that [; mq = m ;], and an *r* such that [; rm = m ;] (with *r* and *q* also being such linear combinations)
I also feel like I'm super close to finding some *f* to the real numbers such that [; f(mn) = f(m) * f(n) ;] (like a determinant of sorts), but I can't quite figure it out. I just don't have the tools to work with a structure that is neither associative nor commutative.
I think that if I could read some material about magmas, I could have a breakthrough. I just don't know what to read, especially when I don't have any background in mathematics.
Does anyone have any recommendations?
#science
I'm a hobbyist in math, so I mostly only know things that I could learn on youtube and the limited amount of info I could learn from wikipedia.
I'm really interested in learning more about magmas where there's no identity element, and every element is idempotent.
I've played around with linear combinations of a magma consisting of
\* | i | j | k
-|-|-|-
**i** | i | k | -j
**j** | -k | j | i
**k** | j | -i | k
so: [; m = ai + bj + ck; a,b,c ∈ ℝ ;]
And I think I figured out that most of these *m* have and element *q*, such that [; mq = m ;], and an *r* such that [; rm = m ;] (with *r* and *q* also being such linear combinations)
I also feel like I'm super close to finding some *f* to the real numbers such that [; f(mn) = f(m) * f(n) ;] (like a determinant of sorts), but I can't quite figure it out. I just don't have the tools to work with a structure that is neither associative nor commutative.
I think that if I could read some material about magmas, I could have a breakthrough. I just don't know what to read, especially when I don't have any background in mathematics.
Does anyone have any recommendations?
#science
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