Journal of Generalized Lie Theory and Applications

We introduce a new kind of a fuzzy Lie subalgebra of a Lie algebra called, an (; )- fuzzy Lie subalgebra and investigate some of its properties. We also present characterization theorems of implication-based fuzzy Lie subalgebras.

It is shown that the non-associative operators in a non-associative quantum theory are unobservables. The observable quantity may be presented only by the elements of some asso- ciative subalgebra. It is shown that the elements of the associative subalgebra are extended objects that can be similar to strings. It is assumed that the non-associative quantum eld theory can be applied to the quantization of strongly interacting elds. The method for obtaining eld equations in a non-associative case is given.

We investigate properties of commutative subrings and ideals in non-commutative algebraic crossed products for actions by arbitrary groups. A description of the commutant of the coecient subring in the crossed product ring is given. Conditions for commutativity and maximal commutativity of the commutant of the coecient subring are provided in terms of the action as well as in terms of the intersection of ideals in the crossed product ring with the coecient subring, specially taking into account both the case of coecient rings without non-trivial zero-divisors and the case of coecient rings with non-trivial zero-divisors.