noncommutative ring
1Noncommutative ring — In mathematics, more specifically modern algebra and ring theory, a noncommutative ring is a ring whose multiplication is not commutative; that is, if R is a noncommutative ring, there exists a and b in R with a·b ≠ b·a, and conversely.… …
2Noncommutative algebraic geometry — is a branch of mathematics, and more specifically a direction in noncommutative geometry that studies the geometric properties of formal duals of non commutative algebraic objects such as rings as well as geometric objects derived from them (e.g …
3Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …
4Ring theory — In abstract algebra, ring theory is the study of rings algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their… …
5Noncommutative logic — is an extension of linear logic which combines the commutative connectives of linear logic with the noncommutative multiplicative connectives of the Lambek calculus (see External links below). Its sequent calculus relies on the structure of order …
6Noncommutative topology — in mathematics is a term applied to the strictly C* algebraic part of the noncommutative geometry program. The program has its origins in the Gel fand duality between the topology of locally compact spaces and the algebraic structure of… …
7Noncommutative geometry — Not to be confused with Anabelian geometry. Noncommutative geometry (NCG) is a branch of mathematics concerned with geometric approach to noncommutative algebras, and with construction of spaces which are locally presented by noncommutative… …
8Noncommutative unique factorization domain — In mathematics, the noncommutative unique factorization domain is the noncommutative counterpart of the commutative or classical unique factorization domain (UFD). Example The ring of integral quaternions. If the coefficients a0, a1, a2, a3 are… …
9Domain (ring theory) — In mathematics, especially in the area of abstract algebra known as ring theory, a domain is a ring such that ab = 0 implies that either a = 0 or b = 0.[1] That is, it is a ring which has no left or right zero divisors. (Sometimes such a ring is… …
10Noetherian ring — In mathematics, more specifically in the area of modern algebra known as ring theory, a Noetherian ring, named after Emmy Noether, is a ring in which every non empty set of ideals has a maximal element. Equivalently, a ring is Noetherian if it… …
