Congruences and ideals in ternary rings

Abstract

A ternary ring is an algebraic structure R=(R,t0.1) of type (3, 0, 0) satisfying the identities t(0, x, y) = y = t(x, 0, y) and t(1, x, 0) = x = (x, l, 0) where, moreover, for any a, b, c ∈ R there exists a unique d ∈ R with t(a, b, d) = c. A congruence θ on R is called normal if R with t 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.