Three-dimensional associative non-commutative algebras

[摘要] Every 3-dimensional associative noncommutative algebra A over a field K has a two-dimensional subalgebra. In A there exist commuting, but linearly independent, elements. Therefore the vector product in K-3 cannot be represented as commutator in an associative three-dimensional algebra over K. (C) 2000 Academic Press.

[发布日期] 2000-12-15