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The center of a group is the set of elements which commute with every element of the group. It is equal to the intersection of the centralizers of the group elements.

A Lie groupoid over B is a groupoid G for which G and B are differentiable manifolds and alpha,beta and multiplication are differentiable maps. Furthermore, the derivatives ...

Let N be a nilpotent, connected, simply connected Lie group, and let D be a discrete subgroup of N with compact right quotient space. Then N/D is called a nilmanifold.

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 ...

Given a real m×n matrix A, there are four associated vector subspaces which are known colloquially as its fundamental subspaces, namely the column spaces and the null spaces ...

The identity element of an additive monoid or group or of any other algebraic structure (e.g., ring, module, abstract vector space, algebra) equipped with an addition. It is ...

Given a differential p-form q in the exterior algebra ^ ^pV^*, its envelope is the smallest subspace W such that q is in the subspace ^ ^pW^* subset ^ ^pV^*. Alternatively, W ...

Let A be a commutative ring and let C_r be an R-module for r=0,1,2,.... A chain complex C__ of the form C__:...|->C_n|->C_(n-1)|->C_(n-2)|->...|->C_2|->C_1|->C_0 is said to ...

There are two completely different definitions of Cayley numbers. The first and most commonly encountered type of Cayley number is the eight elements in a Cayley algebra, ...

The number of nonassociative n-products with k elements preceding the rightmost left parameter is F(n,k) = F(n-1,k)+F(n-1,k-1) (1) = (n+k-2; k)-(n+k-1; k-1), (2) where (n; k) ...