Middle nuclear square loop

This article defines a property that can be evaluated for a loop.
View other properties of loops

Definition

Symbol-free definition

An algebra loop is termed a middle nuclear square loop if every square element is in the middle nucleus.

Definition with symbols

An algebra loop $(L,*)$ is termed a middle nuclear square loop if it satisfies the following identity for all $x,y,z\in L$:

$\!x*((y*y)*z)=(x*(y*y))*z$

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Group