We prove that the variety of Lie algebras arising from splicing operation coincides with the variety CM of centreby-metabelian Lie algebras. Using these Lie algebras we find the minimal dimension algebras generated the variety CM and the variety of its associative envelope algebras. We study the splicing n-ary operation. We show that all n-ary (n > 2) commutator algebras arising from this operation are nilpotent of index 3. We investigate the generalization of the splicing n-ary operation, and...

A ternary ring is an algebraic structure $ℛ=(R;t,0,1)$ of type $(3,0,0)$ satisfying the identities $t(0,x,y)=y=t(x,0,y)$ and $t(1,x,0)=x=(x,1,0)$ where, moreover, for any $a$, $b$, $c\in R$ there exists a unique $d\in R$ with $t(a,b,d)=c$. A congruence $\theta$ on $ℛ$ is called normal if $ℛ/\theta$ is a ternary ring again. We describe basic properties of the lattice of all normal congruences on $ℛ$ and establish connections between ideals (introduced earlier by the third author) and congruence kernels.