An extension of the Wedderburn-Artin Theorem

Semisimple Synchronizing Automata and the Wedderburn-Artin Theory

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

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...

The Wedderburn Principal Theorem for Alternative Algebras

for all a, x in 21. I t is clear that associative algebras are alternative. The most famous examples of alternative algebras which are not associative are the so-called Cayley-Dickson algebras of order 8 over $. Let S be an algebra of order 2 over % which is either a separable quadratic field over 5 or the direct sum 5 ©3There is one automorphism z—>z of S (over %) which is not the identity aut...

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.

Witt ’ s Proof of the Wedderburn Theorem 1

The following propositions are true: (1) For every natural number a and for every real number q such that 1 < q and q = 1 holds a = 0. (2) For all natural numbers a, k, r and for every real number x such that 1 < x and 0 < k holds xa·k+r = x · xa·(k− ′1)+r. (3) For all natural numbers q, a, b such that 0 < a and 1 < q and q − 1 | q − 1 holds a | b. (4) For all natural numbers n, q such that 0 <...