division ring, also called a skew field, is a nontrivial ring in which division by nonzero elements is defined. Specifically, it is a nontrivial ring...

Saturn's ring was composed of multiple smaller rings with gaps between them; the largest of these gaps was later named the Cassini Division. This division is...

simplest commutative rings are those that admit division by non-zero elements; such rings are called fields. Examples of commutative rings include the set...

different language, modules, special classes of rings (group rings, division rings, universal enveloping algebras), as well as an array of properties that...

application in projective geometry requires that the scalars come from a division ring (skew field), K, and this means that the "vectors" should be replaced...

Equivalently, a noncommutative ring is a ring that is not a commutative ring. Noncommutative algebra is the part of ring theory devoted to study of properties...

nonzero ring R in which every nonzero element is a unit (that is, R× = R ∖ {0}) is called a division ring (or a skew-field). A commutative division ring is...

leads to the concept of a division ring or skew field; sometimes associativity is weakened as well. The only division rings that are finite-dimensional...

3-sphere. The Hurwitz quaternions form an order (in the sense of ring theory) in the division ring of quaternions with rational components. It is in fact a maximal...

normed division algebras are R, C, H, and the (non-associative) algebra O. Pontryagin variant. If D is a connected, locally compact division ring, then...