Algebras whose right nucleus is a central simple algebra
Susanne Pumpluen

TL;DR
This paper extends classical algebra constructions to nonassociative algebras, demonstrating the existence of algebras with prescribed nuclei and analyzing their properties over various fields.
Contribution
It introduces a method to construct nonassociative algebras with a given central division algebra as their right nucleus, generalizing Amitsur's work to a broader algebraic context.
Findings
Existence of infinite-dimensional nonassociative algebras with prescribed nuclei.
Proof that certain p-algebras are cyclic differential extensions.
Construction of finite-dimensional division algebras with specified nuclei.
Abstract
We generalize Amitsur's construction of central simple algebras over a field which are split by field extensions possessing a derivation with field of constants to nonassociative algebras: for every central division algebra over a field of characteristic zero there exists an infinite-dimensional unital nonassociative algebra whose right nucleus is and whose left and middle nucleus are a field extension of splitting , where is algebraically closed in . We then give a short direct proof that every -algebra of degree , which has a purely inseparable splitting field of degree and exponent one, is a differential extension of and cyclic. We obtain finite-dimensional division algebras over a field of characteristic whose right nucleus is a division -algebra.
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