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In abstract topology, a machine is method for producing infinite loop spaces and spectra. In automata theory, an abstract machine that is implemented in hardware is simply ...

The ring of integers of a number field K, denoted O_K, is the set of algebraic integers in K, which is a ring of dimension d over Z, where d is the extension degree of K over ...

A surface given by the parametric equations x(u,v) = u (1) y(u,v) = v (2) z(u,v) = au^4+u^2v-v^2. (3)

A function for which all critical points are nondegenerate and all critical levels are different.

Two real algebraic manifolds are equivalent iff they are analytically homeomorphic (Nash 1952).

The set of nilpotent elements in a commutative ring is an ideal, and it is called the nilradical. Another equivalent description is that it is the intersection of the prime ...

Let K be a number field of extension degree d over Q. Then an order O of K is a subring of the ring of integers of K with d generators over Z, including 1. The ring of ...

An ordinary double point of a plane curve is point where a curve intersects itself such that two branches of the curve have distinct tangent lines. Ordinary double points of ...

The function f(x,y)=(2x^2-y)(y-x^2) which does not have a local maximum at (0, 0), despite criteria commonly touted in the second half of the 1800s which indicated the ...

Let V be a variety, and write G(V) for the set of divisors, G_l(V) for the set of divisors linearly equivalent to 0, and G_a(V) for the group of divisors algebraically equal ...