Geodesic
Congruences and ideals in ternary rings
Czechoslovak Mathematical Journal, Tome 47 (1997) no. 1, pp. 163-172 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 08A05, 08A30, 13A15, 17A40, 20N10
Keywords: ternary ring; ideal; congruence; normal congruence; congruence kernel 
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Chajda, Ivan; Halaš, Radomír; Machala, František. Congruences and ideals in ternary rings. Czechoslovak Mathematical Journal, Tome 47 (1997) no. 1, pp. 163-172. http://geodesic.mathdoc.fr/item/CMJ_1997_47_1_a12/

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