Explore: Noncommutative Algebra

ba are different. Equivalently, a noncommutative ring is a ring that is not a commutative ring. Noncommutative algebra is the part of ring theory devoted

Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of

Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric

philosophy of noncommutative geometry, which tries to study various non-classical and/or pathological objects by noncommutative operator algebras. Examples

mathematics, especially in the area of abstract algebra known as ring theory, a free algebra is the noncommutative analogue of a polynomial ring since its elements

honor. In the third epoch (1927–1935), she published works on noncommutative algebras and hypercomplex numbers and united the representation theory of

Commutative rings are much better understood than noncommutative ones. Algebraic geometry and algebraic number theory, which provide many natural examples

space X, the *-algebra L∞(X) is a von Neumann algebra. Due to this analogy, the theory of von Neumann algebras has been called noncommutative measure theory

first course in noncommutative rings. Graduate Texts in Mathematics. Vol. 131 (2 ed.). Springer. ISBN 0-387-95183-0. "Division algebra", Encyclopedia of

every algebra. Union and intersection are commutative operations on sets. "And" and "or" are commutative logical operations. Division is noncommutative, since