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An important result in valuation theory which gives information on finding roots of polynomials. Hensel's lemma is formally stated as follows. Let (K,|·|) be a complete ...

Two mathematical objects are said to be homotopic if one can be continuously deformed into the other. For example, the real line is homotopic to a single point, as is any ...

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length b and the remaining side has length a. This property ...

The Jacobi symbol, written (n/m) or (n/m) is defined for positive odd m as (n/m)=(n/(p_1))^(a_1)(n/(p_2))^(a_2)...(n/(p_k))^(a_k), (1) where m=p_1^(a_1)p_2^(a_2)...p_k^(a_k) ...

In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...

The Kronecker-Weber theorem, sometimes known as the Kronecker-Weber-Hilbert theorem, is one of the earliest known results in class field theory. In layman's terms, the ...

Given a 111×111 (0,1)-matrix, fill 11 spaces in each row in such a way that all columns also have 11 spaces filled. Furthermore, each pair of rows must have exactly one ...

An algebra <L; ^ , v > is called a lattice if L is a nonempty set, ^ and v are binary operations on L, both ^ and v are idempotent, commutative, and associative, and they ...

A continuous distribution in which the logarithm of a variable has a normal distribution. It is a general case of Gibrat's distribution, to which the log normal distribution ...

Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix--a so-called diagonal matrix--that shares the same fundamental ...