Seja d:= \'\\partial\'/\'\\partial IND.x\'+ \'beta\\partial\'/\'partial IND.y\'uma derivação simples de K[x,y], onde K é um corpo de característica zero. Doering, Lequain e Ripoll ([1]) provaram que exite um \'gama\'\'PERTENCE A\' K[x,y] tal que o operador S = \'\\partial\'/\'\\partial x\'+\'beta\\partial\'/\'\\partial y\'+\'gama\'\'PERTENCE A\'\'A IND.2\'\':= K[x,y]\' < \'\\partial\'/partial IND.x\', \'\\partial\'/\'partial\'/\'partial IND y\'\'>\'gera um ideal à esquerda maximal principal de \'A IND.2\'. Desta maneira mostraram, para n=2, que a seguinte conjectura é verdadeira: Seja d:=\'\\partial\'/ \'\\partial IND.x\"IND.1\"+\"alfa\'IND.2\'\'\\partial\'/\'\\partial\'IND.x\'\'IND.2\"+...+ alfa IND.n\"\\partial\'/\'\\partial IND.x\'\'IND.n\" uma derivaçào simples de K[\'x IND.1\'...\'x IND n\']. Então, A IND.n\'(d+\'gama\') é um ideal à esquerda maximal principal de Á IND.n\', para algum \'gama\'\'PERTENCE A\'K[\'x IND.1\',...\'x IND.n\']. Nós mostramos que esta conjectura é verdadeira em alguns casos particulares / Let d: =\'\\partial/\'/\'\\partial IND.x\'+ \'beta\\partial IND.y\' be a simple derivation of K[x,y], where K is a field of characteristic zero. Doering, Lequain e Ripol ([1]) proved that there exists a polynomial um \'gama\'\'IT BELONGS\' K[x,y] such that the operador S =\'\\partial\'/\'\\partial x\'+\'beta\\partial\'/\'\\partial y\'\'gama\'\'IT BELONGS\'\' á ind.2\':= K[x,y]\' < \'\\partial\'/\'partial IND.x\',\'partial\'/\'partial\'/\'partial IND y\'> \'generates a principal maximal left ideal of A IND.2\'. In this way, they showed that, for n=2, the following conjectures is tru: Let d:=\'\\partial\'/\'\\partial IND.x\"+\"alfaÍND.2\"\\partial\'/ \"\\partial\' IND.x\'IND.2\"+ álfa IND.n\"\\partial IND.xÍND.n\"be a simple derivation of K[\'x IND.1\',...,\'x IND n\']. Then, \'A IND.n\'(d+\'gama\') is a principal maximal left ideal of \'A IND.n\',for some \'gama\"IT BELONGS\'K[x IND.1\',...,\'x IND.n\']. We show that this conjecture is true in some cases

Seja d:= \'\\partial\'/\'\\partial IND.x\'+ \'beta\\partial\'/\'partial IND.y\'uma derivação simples de K[x,y], onde K é um corpo de característica zero. Doering, Lequain e Ripoll ([1]) provaram que exite um \'gama\'\'PERTENCE A\' K[x,y] tal que o operador S = \'\\partial\'/\'\\partial x\'+\'beta\\partial\'/\'\\partial y\'+\'gama\'\'PERTENCE A\'\'A IND.2\'\':= K[x,y]\' < \'\\partial\'/partial IND.x\', \'\\partial\'/\'partial\'/\'partial IND y\'\'>\'gera um ideal à esquerda maximal principal de \'A IND.2\'. Desta maneira mostraram, para n=2, que a seguinte conjectura é verdadeira: Seja d:=\'\\partial\'/ \'\\partial IND.x\"IND.1\"+\"alfa\'IND.2\'\'\\partial\'/\'\\partial\'IND.x\'\'IND.2\"+...+ alfa IND.n\"\\partial\'/\'\\partial IND.x\'\'IND.n\" uma derivaçào simples de K[\'x IND.1\'...\'x IND n\']. Então, A IND.n\'(d+\'gama\') é um ideal à esquerda maximal principal de Á IND.n\', para algum \'gama\'\'PERTENCE A\'K[\'x IND.1\',...\'x IND.n\']. Nós mostramos que esta conjectura é verdadeira em alguns casos particulares / Let d: =\'\\partial/\'/\'\\partial IND.x\'+ \'beta\\partial IND.y\' be a simple derivation of K[x,y], where K is a field of characteristic zero. Doering, Lequain e Ripol ([1]) proved that there exists a polynomial um \'gama\'\'IT BELONGS\' K[x,y] such that the operador S =\'\\partial\'/\'\\partial x\'+\'beta\\partial\'/\'\\partial y\'\'gama\'\'IT BELONGS\'\' á ind.2\':= K[x,y]\' < \'\\partial\'/\'partial IND.x\',\'partial\'/\'partial\'/\'partial IND y\'> \'generates a principal maximal left ideal of A IND.2\'. In this way, they showed that, for n=2, the following conjectures is tru: Let d:=\'\\partial\'/\'\\partial IND.x\"+\"alfaÍND.2\"\\partial\'/ \"\\partial\' IND.x\'IND.2\"+ álfa IND.n\"\\partial IND.xÍND.n\"be a simple derivation of K[\'x IND.1\',...,\'x IND n\']. Then, \'A IND.n\'(d+\'gama\') is a principal maximal left ideal of \'A IND.n\',for some \'gama\"IT BELONGS\'K[x IND.1\',...,\'x IND.n\']. We show that this conjecture is true in some cases