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Keywords:
ternary ring; ideal; congruence; normal congruence; congruence kernel
ternary ring; ideal; congruence; normal congruence; congruence kernel
Summary:
A ternary ring is an algebraic structure ${\mathcal R}=(R;t,0,1)$ 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 ${\mathcal R}$ is called normal if ${\mathcal R}/\theta $ is a ternary ring again. We describe basic properties of the lattice of all normal congruences on ${\mathcal R}$ and establish connections between ideals (introduced earlier by the third author) and congruence kernels.
References:
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