All Questions
Tagged with self-distributivity universal-algebra
7 questions
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2
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Example of idempotent left quasigroups which are right-distributive but not left-distributive
I am looking for examples of the following algebraic structure: a set (X,.) which satisfy the axioms
(idempotent) x.x = x
(left quasigroup) the equation a.x = b has a unique solution denoted by x = ...
- 785
1
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Basic questions about varieties of uniformly partially permutative algebras
Define the Fibonacci terms $t_{n}(x,y)$ for all $n\geq 1$ by letting
$t_{1}(x,y)=y,t_{2}(x,y)=x,t_{n+2}(x,y)=t_{n+1}(x,y)*t_{n}(x,y)$.
We say that an algebra $(X,*)$ is $N$-uniformly partially ...
1
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Which varieties are compatible with the classical Laver tables?
Let $$A_{n}=(\{1,\dots,2^{n}-1,2^{n}\},*_{n})$$ denote the $n$-th classical Laver table. The operation $*_{n}$ is the unique binary operation on
$\{1,\dots,2^{n}\}$ such that $$x*_{n}(y*_{n}z)=(x*_{n}...
6
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Can finite binary self-distributive algebras fit into small $n$-ary self-distributive algebras?
A binary operation $*$ is said to be self-distributive if it satisfies the identity $x*(y*z)=(x*y)*(x*z)$. An $n+1$-ary operation $t$ is said to be self-distributive if it satisfies the identity
$$t(...
4
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How many compatible linear orders exist on the classical Laver tables?
Let $A_{n}$ be the unique algebra $(\{1,\dots,2^{n}\},*_{n})$ such that
$x*_{n}1=x+1\mod 2^{n}$ and
$x*_{n}(y*_{n}z)=(x*_{n}y)*_{n}(x*_{n}z)$ for all $x,y,z$. We say that a linear ordering $\preceq$ ...
7
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Hemi-semi direct product of racks or quandles
In the category of racks (similarly quandles), instead of well-known semidirect product, we have the hemi-semi direct product construction as seen on Wagemann & Crans.
As far as I know, semi ...
- 191
16
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2
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Formally undecidable problems on finitely presented quandles
In the literature, one sometimes sees the claim that finitely presented quandles (in particular, knot quandles) are "hard to deal with". Hence, a great deal of effort has gone into studying finite ...
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