Determinants and limit systems in some idempotent and non-associative algebraic structure

This paper considers an idempotent and symmetrical algebraic structure as well some closely related concepts. A special notion of determinant is introduced a Cramer formula derived for class limit systems from the Hadamard matrix product. Thereby, standard results arising Max-Times with nonnegative entries appear case. The case two sided also analyzed. In addition, eigenvalue in considered. It shown that one can construct semi-continuous regularized polynomial whose zeros are to eigenvalues entries.