An approximation theorem for Dubrovin valuation rings.
An embedding theorem for free associative algebras.
Bezout orders.
Constructions and homological properties of simple von Neumann regular rings
Division Rings and Group von Neumann Algebras.
Linearly compact chain rings.
Notes on Whitehead space of an algebra.
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 ordered division rings
Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel’s axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under for nonzero , instead of requiring that positive elements have a positive product. In this work, this type of ordering is studied in the case of a division ring. It is shown that it actually behaves the same as in the commutative...
Representing idempotents as a sum of two nilpotents - an approach via matrices over division rings
Subgroups of finite index in an additive group of a ring.
The upper central series of some matrix groups
Über die Existenz maximaler algebraischer Körperweiterungen.
Алгебраически замкнутое тело Макар-Лиманова
Клиффордовы моноиды и булевозначные группы с нулем
О конечночти в регулярных кольцах
О различных определениях алгебраически замкнутых тел