Malcev-Moduln.
Minimally nonassociative Moufang loops with a unique nonidentity commutator are ring alternative
We investigate finite Moufang loops with a unique nonidentity commutator which are not associative, but all of whose proper subloops are associative. Curiously, perhaps, such loops turn out to be ``ring alternative'', in the sense that their loop rings are alternative rings.
Moduln und Radikale von nichtassoziativen Ringen.
Moufang H*-algebras.
Nichtausgeartete Kompositionsalgebren vom Grad 3.
Nonassociative algebras with submultiplicative bilinear form.
Octave recurrence relations
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 the Scole of a Noncommutative Jordan Algebra.
On the Specht property of varieties of commutative alternative algebras over a field of characteristic 3 and commutative Moufang loops.
Orthogonally complete alternative rings.
Places of alternative fields
Prime factorization of integral Cayley octaves
Radikale von separablen Algebren über Ringen.
Reversibility in absolute-valued algebras
Right Alternative Rings with Minimal Condition.
Some examples of real division algebras.
Strongly prime alternative pairs with minimal inner ideals.
Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions
This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra of the symmetric group over a field of characteristic 0 (or ). The goal is to obtain a constructive version of the isomorphism where is a partition of and counts the standard tableaux of shape ....