Notes on Galois extensions with inner Galois groups.
On a characterization of Azumaya algebras.
A direct proof of Braun's characterization of Azumaya algebras is given.
On a class of free Galois extensions.
On abelian separable extensions and Galois sets of rings
On automorphisms of quaternion orders.
On Azumaya algebras with a finite automorphism group.
On Azumaya Galois extensions and skew group rings.
On center-like elements in rings.
On central commutator Galois extensions of rings.
On certain classes of Galois extensions of rings.
On characterizations of a center Galois extension.
On classification of semigroup rings.
On discriminants and indices of integers of an algebraic number field.
On Free Quadratic Extensions of Rings.
On free subgroups of units in quaternion algebras
It is well known that for the ring H(ℤ) of integral quaternions the unit group U(H(ℤ) is finite. On the other hand, for the rational quaternion algebra H(ℚ), its unit group is infinite and even contains a nontrivial free subgroup. In this note (see Theorem 1.5 and Corollary 2.6) we find all intermediate rings ℤ ⊂ A ⊆ ℚ such that the group of units U(H(A)) of quaternions over A contains a nontrivial free subgroup. In each case we indicate such a subgroup explicitly. We do our best to keep the arguments...
On free subgroups of units in quaternion algebras II
Let A ⊆ ℚ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra H(A) to units of certain rings of generalized quaternions H(A,a,b) = ((-a,-b)/A), where a,b ∈ A. Next we show that there is an algebra embedding of the ring H(A,a,b) into the algebra of standard Cayley numbers over A. Using this embedding we answer a question asked in the first part of this paper.
On Galois projective group rings.
On generalized quaternion algebras.
On -separable and Galois extensions of rings.
On Hopf DeMeyer-Kanzaki Galois extensions.