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A finite division algebra is a field.

The double-struck capital letter I, I, is a symbol sometimes used instead of Z for the ring of integers. In contrast, the lower case symbol i is used to refer to the ...

"The" Jacobi identity is a relationship [A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0,, (1) between three elements A, B, and C, where [A,B] is the commutator. The elements of a Lie algebra ...

One of the operations of addition, subtraction, multiplication, division, and integer (or rational) root extraction.

A set which contains a nonnegative integral number of elements is said to be finite. A set which is not finite is said to be infinite. A finite or countably infinite set is ...

Model completion is a term employed when existential closure is successful. The formation of the complex numbers, and the move from affine to projective geometry, are ...

Let G be a group and theta n permutation of G. Then theta is an orthomorphism of G if the self-mapping nu of G defined by nu(x)=x^(-1)theta(x) is also an permutation of G.

A reduced root system is a root system R satisfying the additional property that, if alpha in R, then the only multiples of alpha in R are +/-alpha.

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these ...

The axiom of Zermelo-Fraenkel set theory which asserts that sets formed by the same elements are equal, forall x(x in a=x in b)=>a=b. Note that some texts (e.g., Devlin ...