In algebra, a division ring, also called a skew field (or, occasionally, a sfield), is a nontrivial ring in which division by nonzero elements is defined...

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...

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...

different language, modules; special classes of rings (group rings, division rings, universal enveloping algebras); related structures like rngs; as well...

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...

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...

characterizes every simple Artinian ring as a ring of matrices over a division ring. This implies that a simple ring is left Artinian if and only if it...

decomposition of a ring: for example, a ring is semisimple if and only if it is a direct sum (in fact a product) of matrix rings over division rings (this observation...

mathematics, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism is...