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Krasner's lemma states that if K a complete field with valuation v, K^_ is a fixed algebraic closure of K together with the canonical extension of v, and K^_^^ is its ...

If R is a ring (commutative with 1), the height of a prime ideal p is defined as the supremum of all n so that there is a chain p_0 subset ...p_(n-1) subset p_n=p where all ...

The dilogarithm identity Li_2(-x)=-Li_2(x/(1+x))-1/2[ln(1+x)]^2.

A distinct (including reflections and rotations) arrangement of adjacent squares on a grid, also called a fixed polyomino.

A point at the intersection of two or more grid lines in a point lattice.

Let K be a finite complex, let h:|K|->|K| be a continuous map. If Lambda(h)!=0, then h has a fixed point.

Let suma_k and sumb_k be two series with positive terms and suppose lim_(k->infty)(a_k)/(b_k)=rho. If rho is finite and rho>0, then the two series both converge or diverge.

If algebraic integers alpha_1, ..., alpha_n are linearly independent over Q, then e^(alpha_1), ..., e^(alpha_n) are algebraically independent over Q. The ...

A link invariant is a function from the set of all links to any other set such that the function does not change as the link is changed (up to isotopy). In other words, a ...

A member of the smallest algebraically closed subfield L of C which is closed under the exponentiation and logarithm operations.