commutative subring
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Subring — In mathematics, a subring is a subset of a ring, which contains the multiplicative identity and is itself a ring under the same binary operations. Naturally, those authors who do not require rings to contain a multiplicative identity do not… … Wikipedia
Subring test — In abstract algebra, the subring test is a theorem that states that for any ring, a nonempty subset of that ring is a subring if it is closed under multiplication and subtraction. Note that here that the terms ring and subring are used without… … Wikipedia
Cayley–Hamilton theorem — In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Hamilton) states that every square matrix over the real or complex field satisfies its own characteristic equation.More precisely; if A is… … Wikipedia
2 × 2 real matrices — The set of 2 × 2 real matrices is denoted by M(2, R). Two matrices p and q in M(2, R) have a sum p + q given by matrix addition. The product matrix p q is formed from the dot product of the rows and columns of its factors… … Wikipedia
Quaternion — Quaternions, in mathematics, are a non commutative extension of complex numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three dimensional space. They find uses in both… … Wikipedia
Real matrices (2 x 2) — The 2 x 2 real matrices are the linear mappings of the Cartesian coordinate system into itself by the rule:(x,y) mapsto (x,y)egin{pmatrix}a c b dend{pmatrix} = (ax + by, cx + dy).The set of all such real matrices is denoted by M(2,R). Two… … Wikipedia
Abelian variety of CM-type — In mathematics, an abelian variety A defined over a field K is said to have CM type if it has a large enough commutative subring in its endomorphism ring End(A). The terminology here is from complex multiplication theory, which was developed for… … Wikipedia
Conformal map — For other uses, see Conformal (disambiguation). A rectangular grid (top) and its image under a conformal map f (bottom). It is seen that f maps pairs of lines intersecting at 90° to pairs of curves still intersecting at 90°. In mathematics, a… … Wikipedia
Center (algebra) — The term center or centre is used in various contexts in abstract algebra to denote the set of all those elements that commute with all other elements. More specifically: * The center of a group G consists of all those elements x in G such that… … Wikipedia
Arrangement of hyperplanes — In geometry and combinatorics, an arrangement of hyperplanes is a finite set A of hyperplanes in a linear, affine, or projective space S . Questions about a hyperplane arrangement A generally concern geometrical, topological, or other properties… … Wikipedia
Ring (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… … Wikipedia
