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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 ...

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(...

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 $\preceq$ ...

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 ...

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}...