algebraic unit
51Glossary of ring theory — Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. Contents 1 Definition of a ring 2 Types of… …
52Split-complex number — A portion of the split complex number plane showing subsets with modulus zero (red), one (blue), and minus one (green). In abstract algebra, the split complex numbers (or hyperbolic numbers) are a two dimensional commutative algebra over the real …
53Local field — In mathematics, a local field is a special type of field that is a locally compact topological field with respect to a non discrete topology.[1] Given such a field, an absolute value can be defined on it. There are two basic types of local field …
54Eigenvalues and eigenvectors — For more specific information regarding the eigenvalues and eigenvectors of matrices, see Eigendecomposition of a matrix. In this shear mapping the red arrow changes direction but the blue arrow does not. Therefore the blue arrow is an… …
55Dual number — For dual grammatical number found in some languages, see Dual (grammatical number). In linear algebra, the dual numbers extend the real numbers by adjoining one new element ε with the property ε2 = 0 (ε is nilpotent). The collection of dual… …
56Complex manifold — In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk[1] in Cn, such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense… …
57Operad theory — is a field of abstract algebra concerned with prototypical algebras that model properties such as commutativity or anticommutativity as well as various amounts of associativity. Operads generalize the various associativity properties already… …
58Irrational number — In mathematics, an irrational number is any real number that is not a rational number that is, it is a number which cannot be expressed as a fraction m / n , where m and n are integers, with n non zero. Informally, this means numbers that cannot… …
59Cubic field — In mathematics, specifically the area of algebraic number theory, a cubic field is an algebraic number field of degree three. Contents 1 Definition 2 Examples 3 Galois closure 4 …
60Covering space — A covering map satisfies the local triviality condition. Intuitively, such maps locally project a stack of pancakes above an open region, U, onto U. In mathematics, more specifically algebraic topology, a covering map is a continuous surjective… …
