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A trace form on an arbitrary algebra A is a symmetric bilinear form (x,y) such that (xy,z)=(x,yz) for all x,y,z in A (Schafer 1996, p. 24).

The algebra structure of linear functionals on polynomials of a single variable (Roman 1984, pp. 2-3).

A Lie algebra is a vector space g with a Lie bracket [X,Y], satisfying the Jacobi identity. Hence any element X gives a linear transformation given by ad(X)(Y)=[X,Y], (1) ...

A bounded entire function in the complex plane C is constant. The fundamental theorem of algebra follows as a simple corollary.

A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...

A local Banach algebra A is stably unital if the collection M_infty(A) of square infinite-dimensional matrices with entries in A has an approximate identity consisting of ...

A Lie algebra is said to be simple if it is not Abelian and has no nonzero proper ideals. Over an algebraically closed field of field characteristic 0, every simple Lie ...

Given a succession of nonsingular points which are on a nonhyperelliptic curve of curve genus p, but are not a group of the canonical series, the number of groups of the ...

Given algebraic numbers a_1, ..., a_n it is always possible to find a single algebraic number b such that each of a_1, ..., a_n can be expressed as a polynomial in b with ...

The Risch algorithm is a decision procedure for indefinite integration that determines whether a given integral is elementary, and if so, returns a closed-form result for the ...