## affine algebraic

35 examples (0.01 sec)
• This is necessary if one wanted the quotient to be an affine algebraic variety.
• An affine algebraic group is called unipotent if all its elements are unipotent.
• For that reason a concept of affine algebraic group is redundant over a field -- we may as well use a very concrete definition.
• One kind is an algebraic group, typically an extension of an abelian variety by an affine algebraic group.
• If G is an affine algebraic group then G/G 0 is actually a finite group.
• These sets of simultaneous solutions are called affine algebraic sets.
• In case G is a linear algebraic group, it is an affine algebraic variety in affine N-space.
• Affine varieties can be given a natural topology by declaring the closed sets to be precisely the affine algebraic sets.
• In a similar way one can define an affine algebraic supergroup as a group object in the category of super algebraic affine varieties.
• A unipotent affine algebraic group is one all of whose elements are unipotent (see below for the definition of an element being unipotent in such a group).
• An affine algebraic supergroup has a similar one to one relation to its Hopf algebra of super Polynomials.
• For any affine algebraic set V, the coordinate ring or structure ring of V is the quotient of the polynomial ring by this ideal.
• A more obvious difference between the two concepts arises because the identity component of an affine algebraic group G is necessarily of finite index in G.
• Similarly, an affine algebraic hypersurface may be defined by an equation, where F is a polynomial.
• In mathematics, the Hochschild-Mostow group, introduced by, is the universal pro-affine algebraic group generated by a group.
• In mathematics, an algebraic torus is a type of commutative affine algebraic group.
• In mathematics, a pseudo-reductive group or k-reductive group over a field k is a smooth connected affine algebraic group defined over k whose unipotent k-radical is trivial.
• Like for affine algebraic sets, there is a bijection between the projective algebraic sets and the reduced homogeneous ideals which define them.
• Complex manifolds that can be embedded in C n are called Stein manifolds and form a very special class of manifolds including, for example, smooth complex affine algebraic varieties.
• The regular maps are also called morphisms, as they make the collection of all affine algebraic sets into a category, where the objects are the affine algebraic sets and the morphisms are the regular maps.