In algebra, a noncommutative Jordan algebra is an algebra, usually over a field of characteristic not 2, such that the four operations of left and right...

necessarily associative", just as "noncommutative" means "not necessarily commutative" for noncommutative rings. An algebra is unital or unitary if it has...

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

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...

one of the motivations for the noncommutative topology and noncommutative geometry programs. Given a Banach *-algebra A with an approximate identity,...

is known as noncommutative algebra; it includes ring theory, representation theory, and the theory of Banach algebras. Commutative algebra is essentially...

coordinate ring of an affine algebraic variety, and the ring of integers of a number field. Examples of noncommutative rings include the ring of n ×...

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...

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

commutativity assumption is a subject matter of noncommutative algebraic geometry and, more recently, of derived algebraic geometry. See also: Generic matrix ring...

this algebra yields as corollaries the various canonical forms of matrices, such as Jordan canonical form. In some approaches to noncommutative geometry...

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

coefficients in the commutative ring R is the free commutative R-algebra of rank n, the noncommutative polynomial ring in n variables with coefficients in the...

mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...

his Ph.D. from Yale University in 1965 with thesis Norms and Noncommutative Jordan Algebras supervised by Nathan Jacobson. McCrimmon spent his final year...

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

has a non-trivial invariant subspace, the fundamental theorem of noncommutative algebra asserts that Lat(Σ) contains non-trivial elements for certain Σ...

(mathematics) Commutative algebra, Commutative ring Ring theory, Noncommutative ring Algebra over a field Non-associative algebra Relatives to rings: Semiring...

mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...

classification of simple Jordan algebras. A Hurwitz algebra or composition algebra is a finite-dimensional not necessarily associative algebra A with identity...

In algebra, the kernel of a homomorphism is the relation describing how elements in the domain of the homomorphism become related in the image. A homomorphism...

reference was mentioned in "Coproduct in the category of (noncommutative) associative algebras". Stack Exchange. May 9, 2012. "How to construct the coproduct...

In algebra, a semiprimitive ring or Jacobson semisimple ring or J-semisimple ring is a ring whose Jacobson radical is zero. This is a type of ring more...

(self-adjoint elements of the C*-algebra) to their expected measurement outcome (real number). States can be viewed as noncommutative generalizations of probability...

split-octonions, like the octonions, are noncommutative and nonassociative. Also like the octonions, they form a composition algebra since the quadratic form N is...

infinite-dimensional Lie algebras. A basic example of a noncommutative vertex algebra is the rank 1 free boson, also called the Heisenberg vertex operator algebra. It is...

Garrett (1967). Algebra. New York: The Macmillan Co. ISBN 1-56881-068-7. MR 0214415. McConnell, J.C.; Robson, J.C., Noncommutative Noetherian Rings,...

In abstract algebra, a semiring is an algebraic structure. Semirings are a generalization of rings, dropping the requirement that each element must have...

Press, ISBN 9780521845045 Rowen, Louis Halle (2008), Graduate Algebra: noncommutative view, Providence, RI: American Mathematical Society, ISBN 978-0-8218-4153-2...