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Let U=(U,<··>) be a T2 associative inner product space over the field C of complex numbers with completion H, and assume that U comes with an antilinear involution xi|->xi^* ...

A mathematical structure (e.g., a group, vector space, or smooth manifold) in a category.

The definition of a set by enumerating its members. An extensional definition can always be reduced to an intentional one. An extension field is sometimes also called simply ...

A nonzero ring S whose only (two-sided) ideals are S itself and zero. Every commutative simple ring is a field. Every simple ring is a prime ring.

Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, ...

The twist of a ribbon measures how much it twists around its axis and is defined as the integral of the incremental twist around the ribbon. A formula for the twist is given ...

A separable extension K of a field F is one in which every element's algebraic number minimal polynomial does not have multiple roots. In other words, the minimal polynomial ...

Given two additive groups (or rings, or modules, or vector spaces) A and B, the map f:A-->B such that f(a)=0 for all a in A is called the zero map. It is a homomorphism in ...

Characteristic classes are cohomology classes in the base space of a vector bundle, defined through obstruction theory, which are (perhaps partial) obstructions to the ...

A gadget defined for complex vector bundles. The Chern classes of a complex manifold are the Chern classes of its tangent bundle. The ith Chern class is an obstruction to the ...