Adjective
noncommutative (not comparable)
(of an algebraic structure) Not having commutativity of all elements under its operation.
In noncommutative ring theory, a maximal right ideal is defined analogously as being a maximal element in the poset of proper right ideals, and similarly, a maximal left ideal is defined to be a maximal element of the poset of proper left ideals. Source: Internet
;Column order significance :The order of columns in an SQL table is defined and significant, one consequence being that SQL's implementations of Cartesian product and union are both noncommutative. Source: Internet
For example, most Banach algebras are noncommutative. Source: Internet
For n > 1 (and R not the zero ring), this matrix ring is noncommutative. Source: Internet
His mathematical specialties were noncommutative ring theory and computational algebra and its applications, including automated theorem proving in geometry. Source: Internet
Multiplication is defined by the rules that the elements of G commute with the elements of R and multiply together as they do in the group G. * Many rings that appear in analysis are noncommutative. Source: Internet