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Let K be a number field and let O be an order in K. Then the set of equivalence classes of invertible fractional ideals of O forms a multiplicative Abelian group called the ...

A map defined by one or more polynomials. Given a field K, a polynomial map is a map f:K^n->K^m such that for all points (x_1,...,x_n) in K^n, ...

The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...

An n-tuple, sometimes simply called a "tuple" when the number n is known implicitly, is another word for a list, i.e., an ordered set of n elements. It can be interpreted as ...

A subset B of a vector space E is said to be balanced if lambdaB subset= B whenever lambda is a scalar satisfying |lambda|<=1. Here, the notation lambdaB denotes the set ...

Let X be a topological vector space and for an arbitrary point x in X, denote by N_(x) the collection of all neighborhoods of x in X. A local base at x is any set B subset ...

A line along a normal vector (i.e., perpendicular to some tangent line). If K subset R^d is a centrosymmetric set which has a twice differentiable boundary, then there are ...

Let x be a point in an n-dimensional compact manifold M, and attach at x a copy of R^n tangential to M. The resulting structure is called the tangent space of M at x and is ...

A lucky number of Euler is a number p such that the prime-generating polynomial n^2-n+p is prime for n=1, 2, ..., p-1. Such numbers are related to the imaginary quadratic ...

For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...