Ideais de anéis de operadores diferenciais / Ideals of rings of differential operators
AUTOR(ES)
Napoleon Caro Tuesta
FONTE
IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia
DATA DE PUBLICAÇÃO
07/04/2011
RESUMO
In [12] J.T. Stafford proved that every left or right ideal of the Weyl algebra \ A IND. n\ (K) = K[\ x IND. 1\ , ...\ x IND. n\ ](\ partial IND. 1, ...\ partial IND. n\ )(K a field of characteristic zero) is generated by two elements. Consider the ring \ D IND. n\ := K[[\ x IND. 1\ , ...\ x IND.n\ ]](\ partial IND. 1\", ...\ partial IND. n) of differential operators over the ring of formal power series K[[\ x IND. 1\ , ... \ x IND. n\ ]]: A natural question is that if every left or right ideal of \ D IND. n\ (K) can be generated by two elements. In this work we will prove that every left or right ideal of the ring \ E IND. n\ (K) := K((\ x IND. 1\ , ... \ x IND. n\ ))(\ partial IND. 1,...\ partial IND. n\ ) of differential operators over the field of formal Laurent series K((\ x IND. 1\ , ...\ x IND. n\ ))) is generated by two elements. We will prove also that every left or right ideal of the ring \ S IND. n -1\"(K) := K((\ x IND. 1\ , ...\ x IND. n\ -1\ ))[[\ x IND. n]](\ paertial IND. 1, ...\ partial IND. n\ ) is generated by two elements and as a corollary we obtain a proof of that every left or right ideal of the ring \ D IND. 1\ (K) is generated by two elements. This is in accordance with the conjecture that says that in a (noncommutative) Noetherian simple ring, every left or right ideal is generated by two elements
ASSUNTO(S)
Álgebras de weyl anéis de operadores ideais ideals power series rings of differential operators séries de pot~encias stafford theorem teorema de stafford weyl algebras
