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An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the ...

If r is a root of the polynomial equation x^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, where the a_is are integers and r satisfies no similar equation of degree <n, then r is called an ...

There are at least two statements which go by the name of Artin's conjecture. If r is any complex finite-dimensional representation of the absolute Galois group of a number ...

In functional analysis, the Banach-Alaoglu theorem (also sometimes called Alaoglu's theorem) is a result which states that the norm unit ball of the continuous dual X^* of a ...

First stated in 1924, the Banach-Tarski paradox states that it is possible to decompose a ball into six pieces which can be reassembled by rigid motions to form two balls of ...

Bézout's theorem for curves states that, in general, two algebraic curves of degrees m and n intersect in m·n points and cannot meet in more than m·n points unless they have ...

A binomial number is a number of the form a^n+/-b^n, where a,b, and n are integers. Binomial numbers can be factored algebraically as ...

A board is a subset of the polygons determined by a number of (usually regularly spaced and oriented) lines. These polygons form the spaces on which "pieces" can be placed ...

Let f:M|->N be a map between two compact, connected, oriented n-dimensional manifolds without boundary. Then f induces a homomorphism f_* from the homology groups H_n(M) to ...

Given two normal subgroups G_1 and G_2 of a group, and two normal subgroups H_1 and H_2 of G_1 and G_2 respectively, H_1(G_1 intersection H_2) is normal in H_1(G_1 ...