Properties of ternary semigroups, groups and algebras are briefly reviewed. It is shown that there exist three types of ternary units. A ternary analog of deformation is shortly discussed. Ternary coalgebras are defined in the most general manner, their classification with respect to the property “to be derived” is made. Three types of coassociativity and three kinds of counits are given. Terna...

Linear codes with large minimal distances are important error correcting codes in information theory. Orthogonal codes have more applications in the other fields of mathematics. In this paper, we study the binary and ternary orthogonal codes generated by the weight matrices on finite-dimensional modules of simple Lie algebras. The Weyl groups of the Lie algebras act on these codes isometrically...

Let C be a clone of operations on a two element set. In [2] we have proved that the first order theory of finite Boolean algebras with distinguish subset closed under C is decidable if and only if C is a clone containing the ternary discriminator function. Decidability of the theories referred to in the abstract is a consequence of the fact, that finite discriminator subsets of products of alge...

Given a ternary relation C on a set U and an algebra A, we present a construction of a convolution algebra A(U,C) of U = (U,C) over A. This generalises bothmatrix algebras and algebras obtained from convolution of monoids. To any class of algebras corresponds a class of convolution structures. Our study cases are the classes of commutative, associative, Lie, and Jordan algebras. In each of thes...

The associator is an alternating trilinear product for any alternative algebra. We study this trilinear product in three related algebras: the associator in a free alternative algebra, the associator in the Cayley algebra, and the ternary cross product on four-dimensional space. This last example is isomorphic to the ternary subalgebra of the Cayley algebra which is spanned by the non-quaternio...

using fixed pointmethods, we investigate approximately higher ternary jordan derivations in banach ternaty algebras via the cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$