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�������պ����ѧѧ�� 1998, Vol. 24 Issue (1) :100-103    DOI:
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Microlocalizations of Modules with Regular Singularities over Filtered Rings
Zhou Meng*
Beijing University of Aeronautics and Astronautics,Dept.of Applied Mathematics and Physics

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ժҪ �˻�R�ϵ�ģ��΢�ֲ����µ�����������������۵�����.Essen֤����Zariski�˻�R�ϵ�ģM�������������,������΢�ֲ���Q\+μ\-S(M)��ΪQ\+μ\-S(R) ģ�Ծ����������,��Q\+μ\-S(M)��ΪR ģ�Ƿ��Ծ������������֪��.����һ�������������,��֤������M������������R ģ��M�ϵľֲ���������,��Q\+μ\-S(M)��ΪR ģ�Ǿ���������ģ.��һ�������½���˸�����.
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Abstract�� The microlocalized properties of a module over a filtered ring R are discussed by many papers in recent years.For example,Essen proved that if M is a module with regular singularities over a Zariski ring R,then its microlocalization Q\+μ\-S(M) is a Q\+μ\-S(R) module with regular singularities.But it is unknown that if Q\+μ\-S(M) is a R module with regular singularities.In this paper the regular singularities of the microlocalization Q\+μ\-S(M) are discussed as an R module while R is a Zariski filtered ring and M is an R module with regular singularities.An answer to the problem in suitable conditions is given.The result is proved that if M is a R module with regular singularities and the localized filtation on M is a good R filtration then the microlocalization Q\+μ\-S(M) of M is a R module with regular singularities.
Keywords�� filtration   ring   module   regular singularities   microlocalization   localized filtration     
Received 1996-06-05;
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����.�˻���΢�ֲ���ģ���������[J]  �������պ����ѧѧ��, 1998,V24(1): 100-103
Zhou Meng.Microlocalizations of Modules with Regular Singularities over Filtered Rings[J]  JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 1998,V24(1): 100-103
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