The Brauer–Cartan–Hua theorem (named after Richard Brauer

Richard Brauer

Richard Dagobert Brauer was a leading German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory...

, Élie Cartan

Élie Cartan

Élie Joseph Cartan was an influential French mathematician, who did fundamental work in the theory of Lie groups and their geometric applications...

, and Hua Luogeng

Hua Luogeng

Hua Luogeng was a Chinese mathematician born in Jintan, Jiangsu. He was the founder and pioneer in many fields in mathematical research. He wrote more than 200 papers and monographs, many of which became classics. Since his sudden death while delivering a lecture at the University of Tokyo, Japan,...

) is a theorem in abstract algebra

Abstract algebra

Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...

 pertaining to division ring

Division ring

In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible. Specifically, it is a non-trivial ring in which every non-zero element a has a multiplicative inverse, i.e., an element x with...

s, which says that given two division rings K ≤ D such that xKx⁻¹ is contained in K for every x not equal to 0 in D, then either K is contained in Z, the center

Center (algebra)

The term center or centre is used in various contexts in abstract algebra to denote the set of all those elements that commute with all other elements. It is often denoted Z, from German Zentrum, meaning "center". More specifically:...

 of D, or K = D. In other words, if the unit group of K is a normal subgroup

Normal subgroup

In abstract algebra, a normal subgroup is a subgroup which is invariant under conjugation by members of the group. Normal subgroups can be used to construct quotient groups from a given group....

of the unit group of D, then either K = D or K is central, .