Algebras whose right nucleus is a central simple algebra
We generalize Amitsur's construction of central simple algebras which
are split by transcendental extensions to nonassociative algebras: for every
central division algebra D over a field F of characteristic zero there exists
an infinite-dimensional unital nonassociative algebra whose right nucleus is D
and whose left and middle nucleus are a transcendental extension of F splitting
D.
We then give a short direct proof that every p-algebra of degree m, which has a
purely inseparable splitting field K of degree m and exponent one, is a
differential extension of K and cyclic.
We obtain finite-dimensional division algebras over a field F of
characteristic p>0 whose right nucleus is a division p-algebra.
S. Pumpluen < susanne.pumpluen@nottingham.ac.uk >