Galois Theory of Simple Rings |
Contents
Topological setting | 1 |
Simple ring | 13 |
Tensor product of algebras | 21 |
14 other sections not shown
Common terms and phrases
A-module A/B is Galois A/B is left A₁ A₂ Accordingly algebra of finite arbitrary element Artinian ring assertion assume automorphism B-basis B-ring B.V-A-irreducible B₁ B₂ bounded degree central simple algebra coincides contained contraction map conversely Corollary cyclic extension division algebra division ring exists an element F-group f-regular intermediate ring finite Galois finite subset Galois and finite Galois extensions Galois group Galois theory h-Galois and locally Hence Hom(T homomorphism infinite inner Galois irreducible isomorphic Kummer extension left algebraic left finite left locally finite left q-system Lemma Let A/B linearly disjoint locally Galois Math matrix units Nagahara non-zero element Okayama Univ outer Galois Proposition q-Galois and left resp ring of A/B simple algebra simple intermediate ring simple ring subset F T₁ Theorem Tominaga topological unital simple subring V₁ V₁(T whence it follows α α