Algebras whose right nucleus is a central simple algebraTools Pumpluen, Susanne (2018) Algebras whose right nucleus is a central simple algebra. Journal of Pure and Applied Algebra, 222 (9). pp. 27732783. ISSN 00224049
AbstractWe generalize Amitsur's construction of central simple algebras over a field F which are split by field extensions possessing a derivation with field of constants F to nonassociative algebras: for every central division algebra D over a field F of characteristic zero there exists an infinitedimensional unital nonassociative algebra whose right nucleus is D and whose left and middle nucleus are a field extension K of F splitting D, where F is algebraically closed in K. We then give a short direct proof that every palgebra 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 finitedimensional division algebras over a field F of characteristic p > 0 whose right nucleus is a division palgebra.
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