Abstract:
Results on the structure of algebras of any finite signature satisfying Capelli identities over fields and Noetherian commutative associative rings are obtained. It is proved that a finitely generated algebra satisfying Capelli identities of some order has a largest solvable ideal. If, in addition, the algebra is semiprime, then it has only finitely many minimal prime ideals. An estimate is given for the nilpotency class of an ideal that is an obstacle to the representability of a finitely generated algebra satisfying Capelli identities.
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