A Wedderburn-Artin-Jacobson structure theorem

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

On a Wedderburn-artin Structure Theory of a Potent Semiring.

Semisimple Synchronizing Automata and the Wedderburn-Artin Theory

On a Theorem of Artin

We determine the epimorphisms A → W from the Artin group A of type Γ onto the Coxeter group W of type Γ, in case Γ is an irreducible Coxeter graph of spherical type, and we prove that the kernel of the standard epimorphism is a characteristic subgroup of A. This generalizes an over 50 years old result of Artin. AMS Subject Classification: Primary 20F36; Secondary 20F55.

The Artin-schreier Theorem

The algebraic closure of R is C, which is a finite extension. Are there other fields which are not algebraically closed but have an algebraic closure which is a finite extension? Yes. An example is the field of real algebraic numbers. Since complex conjugation is a field automorphism fixing Q, and the real and imaginary parts of a complex number can be computed using field operations and comple...