algebraic set
21Algebraic integer — This article deals with the ring of complex numbers integral over Z. For the general notion of algebraic integer, see Integrality .In number theory, an algebraic integer is a complex number which is a root of some monic polynomial (leading… …
22Algebraic extension — In abstract algebra, a field extension L / K is called algebraic if every element of L is algebraic over K , i.e. if every element of L is a root of some non zero polynomial with coefficients in K . Field extensions which are not algebraic, i.e.… …
23Algebraic element — In mathematics, the roots of polynomials are in abstract algebra called algebraic elements. They can be created in a larger structure ( adjoined ), not simply found to exist in a given one. More precisely, if L is a field extension of K then an… …
24algebraic topology — Math. the branch of mathematics that deals with the application of algebraic methods to topology, esp. the study of homology and homotopy. * * * Field of mathematics that uses algebraic structures to study transformations of geometric objects. It …
25algebraic equation — Math. an equation in the form of a polynomial having a finite number of terms and equated to zero, as 2x3 + 4x2 x + 7 = 0. * * * Mathematical statement of equality between algebraic expressions. An expression is algebraic if it involves a finite… …
26Algebraic differential equation — Note: Differential algebraic equation is something different. In mathematics, an algebraic differential equation is a differential equation that can be expressed by means of differential algebra. There are several such notions, according to the… …
27Set theory — This article is about the branch of mathematics. For musical set theory, see Set theory (music). A Venn diagram illustrating the intersection of two sets. Set theory is the branch of mathematics that studies sets, which are collections of objects …
28Algebraic manifold — An algebraic manifold is an algebraic variety which is also a manifold. As such, algebraic manifolds are a generalisation of the concept of smooth curves and surfaces. An example is the sphere, which can be defined as the zero set of the… …
29algebraic geometry — Math. the study of sets that are defined by algebraic equations. [1895 1900] * * * Study of geometric objects expressed as equations and represented by graphs in a given coordinate system. In contrast to Euclidean geometry, algebraic geometry… …
30Algebraic topology (object) — In mathematics, the algebraic topology on the set of group representations from G to a topological group H is the topology of pointwise convergence, i.e. pi converges to p if the limit of pi ( g ) = p ( g ) for every g in G .This terminology is… …
