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Congruences and ideals in ternary rings

Ivan Chajda, Radomír Halaš, František Machala (1997)

Czechoslovak Mathematical Journal

A ternary ring is an algebraic structure = ( 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 R there exists a unique d R with t ( a , b , d ) = c . A congruence θ on is called normal if / θ is a ternary ring again. We describe basic properties of the lattice of all normal congruences on and establish connections between ideals (introduced earlier by the third author) and congruence kernels.

Convex lines in median groups

Milan Kolibiar (1992)

Archivum Mathematicum

There is proved that a convex maximal line in a median group G , containing 0, is a direct factor of G .

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